%-------------------------------------------------------------------------------
% Step 1
%-------------------------------------------------------------------------------

@article{Mu05,
  author =  {M. Mu},
  title =   {{PDE.M}art: A Network-based Problem-solving Environment for {PDE}s},
  journal = {ACM Transactions on Mathematical Software},
  year =    {2005},
  volume =  {31},
  number =  {4},
  pages =   {508--531},
  url =     {https://doi.org/10.1145/1114268.1114272}
}

%-------------------------------------------------------------------------------
% Step 6
%-------------------------------------------------------------------------------

@article{Kel74,
  author =  {R.B. Kellogg},
  title =   {On the {P}oisson equation with intersecting interfaces},
  journal = {Applicable Analysis},
  year  =   {1974},
  volume =  {4},
  number =  {2},
  pages =   {101--129},
  url =     {https://doi.org/10.1080/00036817408839086}
}

%-------------------------------------------------------------------------------
% Step 7
%-------------------------------------------------------------------------------

@article{Li2019,
  author =  {H. Li and X. Zhang},
  title =   {Superconvergence of {C}$^0$-{Q}$^k$ Finite Element Method for Elliptic Equations with Approximated Coefficients},
  journal = {Journal of Scientific Computing},
  year =    {2020},
  month =   dec,
  volume =  {82},
  number =  {1},
  doi =     {10.1007/s10915-019-01102-1},
  url =     {https://doi.org/10.1007/s10915-019-01102-1}
}

%-------------------------------------------------------------------------------
% Step 10
%-------------------------------------------------------------------------------

@incollection{Cangiani2012,
  author =    {A. Cangiani and J. Chapman and E.H. Georgoulis and M. Jensen},
  title =     {Implementation of the Continuous-Discontinuous {G}alerkin Finite Element Method},
  booktitle = {Numerical Mathematics and Advanced Applications 2011},
  publisher = {Springer Berlin Heidelberg},
  year =      {2012},
  month =     nov,
  pages =     {315--322},
  doi =       {10.1007/978-3-642-33134-3_34},
  url =       {https://doi.org/10.1007/978-3-642-33134-3_34}
}

%-------------------------------------------------------------------------------
% Step 14
%-------------------------------------------------------------------------------

@inproceedings{Ban00w,
  author =    {W. Bangerth},
  title =     {Mesh Adaptivity and Error Control for a Finite Element Approximation of the Elastic Wave Equation},
  booktitle = {Proceedings of the Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Waves2000), Santiago de Compostela, Spain, 2000},
  editor =    {Alfredo Berm\'udez and Dolores G\'omez and Christophe Hazard and Patrick Joly and Jean E. Roberts},
  publisher = {SIAM},
  year =      {2000},
  pages =     {725--729}
}

@phdthesis{Ban02,
  author =  {W. Bangerth},
  title =   {Adaptive Finite Element Methods for the Identification of Distributed Parameters in Partial Differential Equations},
  school =  {University of Heidelberg},
  year =    {2002},
  doi =     {10.11588/heidok.00002508},
  url =     {https://doi.org/10.11588/heidok.00002508}
}

@article{BR99b,
  author =  {W. Bangerth and R. Rannacher},
  title =   {Finite element approximation of the acoustic wave equation: Error control and mesh adaptation},
  journal = {East--West Journal of Numerical Mathematics},
  year =    {1999},
  volume =  {7},
  number =  {4},
  pages =   {263--282}
}

@book{BR03,
  author =    {W. Bangerth and R. Rannacher},
  title =     {Adaptive Finite Element Methods for Differential Equations},
  publisher = {Birkh{\"a}user Verlag},
  year =      {2003},
  url =       {https://doi.org/10.1007/978-3-0348-7605-6}
}

@article{BR01a,
  author =  {W. Bangerth and R. Rannacher},
  title =   {Adaptive Finite Element Techniques for the Acoustic Wave Equation},
  journal = {Journal of Computational Acoustics},
  year =    {2001},
  volume =  {9},
  number =  {2},
  pages =   {575--591},
  url =     {https://doi.org/10.1142/S0218396X01000668}
}

@article{BR01,
  author =  {R. Becker and R. Rannacher},
  title =   {An optimal control approach to error estimation and mesh adaptation in finite element methods},
  journal = {Acta Numerica},
  year =    {2001},
  volume =  {10},
  pages =   {1--102},
  url =     {https://doi.org/10.1017/S0962492901000010}
}

@phdthesis{Bec95,
  author =  {R. Becker},
  title =   {An Adaptive Finite Element Method for the Incompressible {N}avier--{S}tokes Equations on Time-dependent Domains},
  school =  {Universit{\"a}t Heidelberg},
  year =    {1995},
  url = {https://katalog.ub.uni-heidelberg.de/titel/9608091}
}

@techreport{Bec98,
  author =      {R. Becker},
  title =       {Weighted Error Estimators for the Incompressible {N}avier--{S}tokes Equations},
  institution = {Universit{\"a}t Heidelberg},
  type =        {Preprint 98-20},
  year =        {1998}
}

@article{BR96r,
  author =  {R. Becker and R. Rannacher},
  title =   {A Feed-Back Approach to Error Control in Finite Element Methods: Basic Analysis and Examples},
  journal = {East--West Journal of Numerical Mathematics},
  volume =  {4},
  year =    {1996},
  pages =   {237--264}
}

@inproceedings{BR95,
  author =    {R. Becker and R. Rannacher},
  title =     {Weighted A Posteriori Error Control in {FE} Methods},
  booktitle = {ENUMATH 97},
  editor =    {H. G. Bock et al.},
  publisher = {World Scientific Publishing, Singapore},
  year =      {1998},
  pages =     {621--637}
}

@article{FK97,
  author =  {C. F{\"u}hrer and G. Kanschat},
  title =   {A posteriori error control in radiative transfer},
  journal = {Computing},
  year =    {1997},
  volume =  {58},
  number =  {4},
  pages =   {317--334},
  url =     {https://doi.org/10.1007/BF02684345}
}

@phdthesis{Har02,
  author =  {R. Hartmann},
  title =   {Adaptive Finite Element Methods for the Compressible {E}uler Equations},
  school =  {Universit{\"a}t Heidelberg},
  year =    {2002}
}

@article{HH01,
  author =    {R. Hartmann and P. Houston},
  title =     {Adaptive Discontinuous {G}alerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws},
  publisher = {SIAM},
  journal =   {Journal on Scientific Computing},
  year =      {2003},
  volume =    {24},
  number =    {3},
  pages =     {979--1004}
}

@article{HH01b,
  author =  {R. Hartmann and P. Houston},
  title =   {Adaptive Discontinuous {G}alerkin Finite Element Methods for the Compressible {E}uler Equations},
  journal = {Journal of Computational Physics},
  year =    {2002},
  volume =  {183},
  number =  {2},
  pages =   {508--532},
  url =     {https://doi.org/10.1137/S1064827501389084}
}

@phdthesis{Kan96,
  author =  {G. Kanschat},
  title =   {Parallel and Adaptive {G}alerkin Methods for Radiative Transfer Problems},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    {1996}
}

@article{RS97,
  author =  {R. Rannacher and F.-T. Suttmeier},
  title =   {A feed-back approach to error control in finite element methods: Application to linear elasticity},
  journal = {Computational Mechanics},
  year =    {1997},
  volume =  {19},
  number =  {5},
  pages =   {434--446},
  url =     {https://doi.org/10.1007/s004660050191}
}

@article{RS98c,
  author =  {R. Rannacher and F.-T. Suttmeier},
  title =   {A posteriori error control in finite element methods via duality techniques: Application to perfect plasticity},
  journal = {Computational Mechanics},
  year =    {1998},
  volume =  {21},
  number =  {2},
  pages =   {123--133},
  url =     {https://doi.org/10.1007/s004660050288}
}

@article{RS99,
  author =  {R. Rannacher and F.-T. Suttmeier},
  title =   {A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    {1999},
  volume =  {176},
  number =  {1},
  pages =   {333--361},
  url =     {https://doi.org/10.1016/S0045-7825(98)00344-2}
}

@phdthesis{Sut96,
  author =  {F.-T. Suttmeier},
  title =   {Adaptive Finite Element Approximation of Problems in Elasto-Plasticity Theory},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    {1996}
}


%-------------------------------------------------------------------------------
% Step 15
%-------------------------------------------------------------------------------


@book{GNS08,
  author =    {I. Griva and S.G. Nash and A. Sofer},
  title =     {Linear and nonlinear optimization},
  publisher = {SIAM},
  year =      {2008},
  edition =   {2nd},
  url =       {https://doi.org/10.1007/978-1-4939-7055-1}
}

@book{NW99,
  author =    {J. Nocedal and S.J. Wright},
  title =     {Numerical Optimization},
  publisher = {Springer, New York},
  year =      {1999},
  series =    {Springer Series in Operations Research},
  url =       {https://doi.org/10.1007%2F978-0-387-40065-5}
}



%-------------------------------------------------------------------------------
% Step 18
%-------------------------------------------------------------------------------

@article{CTZ04,
  author =  {S. Commend and A. Truty and T. Zimmermann},
  title =   {Stabilized finite elements applied to elastoplasticity: I. {M}ixed displacement–pressure formulation},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    {2004},
  volume =  {193},
  number =  {33},
  pages =   {3559--3586},
  url =     {https://doi.org/10.1016/j.cma.2004.01.007}
}

@article{DL05,
  author =  {H.-Y. Duan and Q. Lin},
  title =   {Mixed finite elements of least-squares type for elasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    {2005},
  volume =  {194},
  number =  {9},
  pages =   {1093--1112},
  url =     {https://doi.org/10.1016/j.cma.2004.06.033}
}


% ------------------------------------
% Step 22
% ------------------------------------

@article{SW94,
  author =  {D. Silvester and A. Wathen},
  title =   {Fast iterative solution of stabilised {S}tokes systems. {P}art {II}: Using general block preconditioners},
  journal = {SIAM Journal on Numerical Analysis},
  year =    {1994},
  volume =  {31},
  pages =   {1352--1367},
  url =     {https://doi.org/10.1137/0731070}
}


% ------------------------------------
% Step 27
% ------------------------------------

@phdthesis{fehling2020,
  author    = {M. Fehling},
  title     = {Algorithms for massively parallel generic \textit{hp}-adaptive finite element methods},
  publisher = {Forschungszentrum J{\"u}lich GmbH Zentralbibliothek, Verlag},
  school    = {Bergische Universit{\"a}t Wuppertal},
  year      = {2020},
  volume    = {43},
  pages     = {vii, 78 pp},
  url       = {https://juser.fz-juelich.de/record/878206}
}


% ------------------------------------
% Step 43
% ------------------------------------

@article{Chueh2010,
  doi = {10.1016/j.compfluid.2010.05.011},
  url = {https://doi.org/10.1016/j.compfluid.2010.05.011},
  year = {2010},
  publisher = {Elsevier {BV}},
  volume = {39},
  number = {9},
  pages = {1585--1596},
  author = {C.C. Chueh and M. Secanell and W. Bangerth and N. Djilali},
  title = {Multi-level adaptive simulation of transient two-phase flow in heterogeneous porous media},
  journal = {Computers {\&} Fluids}
}


@Article{KHB12,
  author = 	 {M. Kronbichler and T. Heister and W. Bangerth},
  title = 	 {High Accuracy Mantle Convection Simulation through Modern Numerical Methods},
  journal = 	 {Geophysical Journal International},
  year = 	 {2012},
  volume = 	 {191},
  pages = 	 {12--29}
}


@article{Chueh2013,
  doi = {10.1137/120866208},
  url = {https://doi.org/10.1137/120866208},
  year = {2013},
  publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
  volume = {35},
  number = {1},
  pages = {B149--B175},
  author = {C.C. Chueh and N. Djilali and W. Bangerth},
  title = {An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media},
  journal = {{SIAM} Journal on Scientific Computing}
}


@Book{BrezziFortin,
  author =    {F. Brezzi and M. Fortin},
  title =        {Mixed and Hybrid Finite Element Methods},
  publisher =    {Springer},
  year =         {1991}
}

@Book{Chen2005,
  author =    {Z. Chen},
  title =        {Finite Element Methods and their Applications},
  publisher =    {Springer},
  year =         {2005}
}

@article{GuermondPasquetti2008,
  doi = {10.1016/j.crma.2008.05.013},
  url = {https://doi.org/10.1016/j.crma.2008.05.013},
  year = {2008},
  month = jul,
  publisher = {Elsevier {BV}},
  volume = {346},
  number = {13-14},
  pages = {801--806},
  author = {J.-L. Guermond and R. Pasquetti},
  title = {Entropy-based nonlinear viscosity for Fourier approximations of conservation laws},
  journal = {Comptes Rendus Mathematique}
}

@article{Buckley1942,
  doi = {10.2118/942107-g},
  url = {https://doi.org/10.2118/942107-g},
  year = {1942},
  month = dec,
  publisher = {Society of Petroleum Engineers ({SPE})},
  volume = {146},
  number = {01},
  pages = {107--116},
  author = {S.E. Buckley and M.C. Leverett},
  title = {Mechanism of Fluid Displacement in Sands},
  journal = {Transactions of the {AIME}}
}

@article{Saad1986,
  doi = {10.1137/0907058},
  url = {https://doi.org/10.1137/0907058},
  year = {1986},
  month = jul,
  publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
  volume = {7},
  number = {3},
  pages = {856--869},
  author = {Y. Saad and M.H. Schultz},
  title = {{GMRES}: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems},
  journal = {{SIAM} Journal on Scientific and Statistical Computing}
}

@Book{GolubVanLoan,
  author =    {G.H. Golub and C.F. van Loan},
  title =        {Matrix Computations},
  publisher =    {Johns Hopkins},
  year =         {1996}
}

@Book{Zhang2005,
  author =    {F. Zhang},
  title =        {The Schur Complement and its Applications},
  publisher =    {Springer},
  year =         {2005}
}


% ------------------------------------
% Step 47
% ------------------------------------

@article{Brenner2005,
  author =    {S.C. Brenner and L.-Y. Sung},
  title =     {C$^0$ Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains},
  journal =   {Journal of Scientific Computing},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {2005},
  month =     jun,
  volume =    {22},
  number =    {1},
  pages =     {83--118},
  doi =       {10.1007/s10915-004-4135-7},
  url =       {https://doi.org/10.1007/s10915-004-4135-7}
}


@incollection{Brenner2011,
  author =    {S.C. Brenner},
  title =     {C$^0$ Interior Penalty Methods},
  booktitle = {Lecture Notes in Computational Science and Engineering},
  publisher = {Springer Berlin Heidelberg},
  year =      {2011},
  pages =     {79--147},
  doi =       {10.1007/978-3-642-23914-4_2},
  url =       {https://doi.org/10.1007/978-3-642-23914-4_2}
}

@article{Engel2002,
  author =    {G. Engel and K. Garikipati and T.J.R. Hughes and M.G. Larson and L. Mazzei and R.L. Taylor},
  title =     {Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates,  and strain gradient elasticity},
  journal =   {Computer Methods in Applied Mechanics and Engineering},
  publisher = {Elsevier BV},
  year =      {2002},
  month =     jul,
  volume =    {191},
  number =    {34},
  pages =     {3669--3750},
  doi =       {10.1016/s0045-7825(02)00286-4},
  url =       {https://doi.org/10.1016/s0045-7825(02)00286-4}
}

@article{Brenner2009,
  author =    {S.C. Brenner and T. Gudi and L.-Y. Sung},
  title =     {An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem},
  journal =   {IMA Journal of Numerical Analysis},
  publisher = {Oxford University Press ({OUP})},
  year =      {2009},
  month =     mar,
  volume =    {30},
  number =    {3},
  pages =     {777--798},
  doi =       {10.1093/imanum/drn057},
  url =       {https://doi.org/10.1093/imanum/drn057}
}

@article{Wells2007,
  author =    {G.N. Wells and N.T. Dung},
  title =     {A {C}$^0$ discontinuous {G}alerkin formulation for {K}irchhoff plates},
  journal =   {Computer Methods in Applied Mechanics and Engineering},
  publisher = {Elsevier BV},
  year =      {2007},
  month =     jul,
  volume =    {196},
  number =    {35-36},
  pages =     {3370--3380},
  doi =       {10.1016/j.cma.2007.03.008},
  url =       {https://doi.org/10.1016/j.cma.2007.03.008}
}

% ------------------------------------
% Step 50
% ------------------------------------

@article{karakashian2003posteriori,
  author =    {O.A. Karakashian and F. Pascal},
  title =     {A posteriori error estimates for a discontinuous {G}alerkin approximation of second-order elliptic problems},
  journal =   {SIAM Journal on Numerical Analysis},
  publisher = {SIAM},
  year =      {2003},
  volume =    {41},
  number =    {6},
  pages =     {2374--2399},
  url =       {https://doi.org/10.1137/S0036142902405217}
}

% ------------------------------------
% Step 51
% ------------------------------------

@article {Ngu2012,
    AUTHOR = {N.C. Nguyen and J. Peraire},
     TITLE = {Hybridizable discontinuous {G}alerkin methods for partial differential equations in continuum mechanics},
   JOURNAL = {Journal of Computational Physics},
      YEAR = {2012},
    VOLUME = {231},
    NUMBER = {18},
     PAGES = {5955--5988},
       DOI = {10.1016/j.jcp.2012.02.033},
       URL = {https://doi.org/10.1016/j.jcp.2012.02.033}
}

@incollection{F65,
  author =    {B.X. Fraeijs de Veubeke},
  title =     {Displacement and equilibrium models in the finite element method},
  booktitle = {Stress Analysis},
  publisher = {Wiley, New York},
  editor =    {O.C. Zienkiewicz and G.S. Holister},
  year =      {1965},
  pages =     {275-284},
  URL =       {https://ci.nii.ac.jp/naid/10003737730/en/}
}

@article{G65,
  author =    {R.J. Guyan},
  title =     {Reduction of stiffness and mass matrices},
  journal =   {AIAA Journal},
  publisher = {American Institute of Aeronautics and Astronautics ({AIAA})},
  year  =     {1965},
  month =     feb,
  volume =    {3},
  number =    {2},
  pages =     {380--380},
  doi =       {10.2514/3.2874},
  url =       {https://doi.org/10.2514/3.2874}
}

@article {CGL2009,
    AUTHOR = {B. Cockburn and J. Gopalakrishnan and R. Lazarov},
     TITLE = {Unified hybridization of discontinuous {G}alerkin, mixed, and continuous {G}alerkin methods for second order elliptic problems},
   JOURNAL = {SIAM Journal on Numerical Analysis},
      YEAR = {2009},
    VOLUME = {47},
    NUMBER = {2},
     PAGES = {1319--1365},
       DOI = {10.1137/070706616},
       URL = {https://doi.org/10.1137/070706616}
}

% ------------------------------------
% Step 55
% ------------------------------------

@book{elman2005,
  Author                   = {H.C. Elman and D.J. Silvester and A.J. Wathen},
  Title                    = {Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics},
  Publisher                = {Oxford University Press},
  Year                     = {2005},
  Address                  = {Oxford, New York},
  Series                   = {Numerical Mathematics and Scientific Computation},
  Url                      = {https://doi.org/10.1093/acprof:oso/9780199678792.001.0001}
}

@inproceedings{kovasznay1948laminar,
  author =       {L.I.G. Kovasznay},
  title =        {Laminar flow behind a two-dimensional grid},
  booktitle =    {Mathematical Proceedings of the Cambridge Philosophical Society},
  organization = {Cambridge University Press},
  year =         {1948},
  volume =       {44},
  number =       {1},
  pages =        {58--62},
  url =          {https://doi.org/10.1017/S0305004100023999}
}


% ------------------------------------
% Step 61
% ------------------------------------

@incollection{Wang2019,
  author =    {Z. Wang and G. Harper and P. O'Leary and J. Liu and S. Tavener},
  title =     {deal.{II} Implementation of a Weak {G}alerkin Finite Element Solver for Darcy Flow},
  booktitle = {Lecture Notes in Computer Science},
  publisher = {Springer International Publishing},
  year =      {2019},
  pages =     {495--509},
  doi =       {10.1007/978-3-030-22747-0_37},
  url =       {https://doi.org/10.1007/978-3-030-22747-0_37}
}

% ------------------------------------
% Step 63
% ------------------------------------

@incollection{john2006discontinuity,
  author =    {V. John and P. Knobloch},
  title =     {On discontinuity—capturing methods for convection—diffusion equations},
  booktitle = {Numerical Mathematics and Advanced Applications},
  publisher = {Springer},
  year =      {2006},
  pages =     {336--344},
  url =       {https://doi.org/10.1007/978-3-540-34288-5_27}
}

@article{KanschatNotesIterative,
  author = {G. Kanschat},
  title =  {Notes on Applied Mathematics: Iterative methods, Schwarz preconditioners and multigrid},
  year =   {2015},
  url =    {https://www.mathsim.eu/~gkanscha/notes/C.pdf}
}

@book{smith2004domain,
  author =    {B. Smith and P. Bjorstad and W. Gropp},
  title =     {Domain decomposition: parallel multilevel methods for elliptic partial differential equations},
  publisher = {Cambridge University Press},
  year =      {2004}
}

@book{toselli2006domain,
  author =    {A. Toselli and O. Widlund},
  title =     {Domain decomposition methods-algorithms and theory},
  publisher = {Springer Science \& Business Media},
  year =      {2006},
  volume =    {34},
  url =       {https://doi.org/10.1007/b137868}
}

% ------------------------------------
% Step 66
% ------------------------------------

@book{bebernes1989mathematical,
  author    = {J. Bebernes and D. Eberly},
  title     = {Mathematical Problems from Combustion Theory},
  publisher = {Springer-Verlag, New York, NY},
  year      = {1989},
  volume    = {83},
  series    = {Applied Mathematical Sciences},
  url       = {https://doi.org/10.1007/978-1-4612-4546-9}
}

@phdthesis{castelli2021numerical,
  author    = {G.F. Castelli},
  title     = {Numerical Investigation of {Cahn--Hilliard}-Type Phase-Field Models for Battery Active Particles},
  school    = {Karlsruhe Institute of Technology (KIT)},
  year      = {2021},
  url       = {https://doi.org/10.5445/IR/1000141249}
}

% ------------------------------------
% Step 67
% ------------------------------------

@article{KennedyCarpenterLewis2000,
  author =  {C.A. Kennedy and M.H. Carpenter and R.M. Lewis},
  title =   {Low-storage, explicit {R}unge--{K}utta schemes for the compressible {N}avier--{S}tokes equations},
  journal = {Applied Numerical Mathematics},
  year =    {2000},
  volume =  {35},
  pages =   {177--219},
  doi =     {10.1016/S0168-9274(99)00141-5},
  url =     {https://doi.org/10.1016/S0168-9274(99)00141-5}
}

@article{TseliosSimos2007,
  author =  {K. Tselios and T.E. Simos},
  title =   {Optimized {R}unge--{K}utta methods with minimal dispersion and dissipation for problems arising from computational acoustics},
  journal = {Physics Letters A},
  year =    {2007},
  volume =  {363},
  pages =   {38--48},
  doi =     {10.1016/j.physleta.2006.10.072},
  url =     {https://doi.org/10.1016/j.physleta.2006.10.072}
}

@article{KronbichlerSchoeder2016,
  author =  {M. Kronbichler and S. Schoeder and C. M\"uller and W.A. Wall},
  title =   {Comparison of implicit and explicit hybridizable discontinuous {G}alerkin methods for the acoustic wave equation},
  journal = {International Journal for Numerical Methods in Engineering},
  year =    {2016},
  volume =  {106},
  number =  {9},
  pages =   {712--739},
  doi =     {10.1002/nme.5137},
  url =     {https://doi.org/10.1002/nme.5137}
}

@article{SchoederKormann2018,
  author =  {S. Schoeder and K. Kormann and W.A. Wall and M. Kronbichler},
  title =   {Efficient explicit time stepping of high order discontinuous {G}alerkin schemes for waves},
  journal = {SIAM Journal on Scientific Computing},
  year =    {2018},
  volume =  {40},
  number =  {6},
  pages =   {C803--C826},
  doi =     {10.1137/18M1185399},
  url =     {https://doi.org/10.1137/18M1185399}
}

@article{FehnWallKronbichler2019,
  author =  {N. Fehn and W.A. Wall and M. Kronbichler},
  title =   {A matrix-free high-order discontinuous {G}alerkin compressible {N}avier--{S}tokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows},
  journal = {International Journal for Numerical Methods in Fluids},
  year =    {2019},
  volume =  {89},
  number =  {3},
  pages =   {71--102},
  url =     {https://doi.org/10.1002/fld.4683}
}

@article{KronbichlerKormann2019,
  author =  {M. Kronbichler and K. Kormann},
  title  =  {Fast matrix-free evaluation of discontinuous {G}alerkin finite element operators},
  journal = {ACM Transactions on Mathematical Software},
  year =    {2019},
  volume =  {45},
  number =  {3},
  pages =   {29:1--29:40},
  doi =     {10.1145/3325864},
  url =     {https://doi.org/10.1145/3325864}
}

@article{Gassner2013,
  author =  {G.J. Gassner},
  title =   {A Skew-Symmetric Discontinuous {G}alerkin Spectral Element Discretization and Its Relation to {SBP}-{SAT} Finite Difference Methods},
  journal = {SIAM Journal on Scientific Computing},
  year =    {2013},
  volume =  {35},
  number =  {3},
  pages =   {A1233--A1253},
  doi =     {10.1137/120890144},
  url =     {https://doi.org/10.1137/120890144}
}

% ------------------------------------
% Step 68
% ------------------------------------

@article{Blais2013,
  author =    {B. Blais and J.-P. Braeunig and D. Chauveheid and J.-M. Ghidaglia and R. Loub{\`e}re},
  title =     {Dealing with more than two materials in the {FVCF}--{ENIP} method},
  journal =   {European Journal of Mechanics-B/Fluids},
  publisher = {Elsevier},
  year =      {2013},
  volume =    {42},
  pages =     {1--9},
  url =       {https://doi.org/10.1016/j.euromechflu.2013.05.001}
}

@article{Blais2019,
  author =    {B. Blais and D. Vidal and F. Bertrand and G.S. Patience and J. Chaouki},
  title =     {Experimental Methods in Chemical Engineering: Discrete Element Method--{DEM}},
  journal =   {The Canadian Journal of Chemical Engineering},
  publisher = {Wiley Online Library},
  year =      {2019},
  volume =    {97},
  number =    {7},
  pages =     {1964--1973},
  url =       {https://doi.org/10.1002/cjce.23501}
}

@article{Gassmoller2019,
  author =    {R. Gassm{\"o}ller and H. Lokavarapu and W. Bangerth and E.G. Puckett},
  title =     {Evaluating the accuracy of hybrid finite element/particle-in-cell methods for modelling incompressible {S}tokes flow},
  journal =   {Geophysical Journal International},
  publisher = {Oxford University Press},
  year =      {2019},
  volume =    {219},
  number =    {3},
  pages =     {1915--1938},
  url =       {https://doi.org/10.1093/gji/ggz405}
}


% ------------------------------------
% Step 69
% ------------------------------------

@article {GuermondPopov2016,
    AUTHOR = {J.-L. Guermond and B. Popov},
     TITLE = {Invariant domains and first-order continuous finite element approximation for hyperbolic systems},
   JOURNAL = {SIAM Journal on Numerical Analysis},
      YEAR = {2016},
    VOLUME = {54},
    NUMBER = {4},
     PAGES = {2466--2489},
       DOI = {10.1137/16M1074291},
       URL = {https://doi.org/10.1137/16M1074291}
}

@article {GuermondPopov2016b,
    AUTHOR = {J.-L. Guermond and B. Popov},
     TITLE = {Fast estimation of the maximum wave speed in the {R}iemann problem for the {E}uler equations},
   JOURNAL = {Journal of Computational Physics},
      YEAR = {2016},
    VOLUME = {321},
     PAGES = {908--926},
       DOI = {10.1016/j.jcp.2016.05.054},
       URL = {https://doi.org/10.1016/j.jcp.2016.05.054}
}

@article {GuermondEtAl2018,
    AUTHOR = {J.-L. Guermond and M. Nazarov and B. Popov and I. Tomas},
     TITLE = {Second-order invariant domain preserving approximation of the {E}uler equations using convex limiting},
   JOURNAL = {SIAM Journal on Scientific Computing},
      YEAR = {2018},
    VOLUME = {40},
    NUMBER = {5},
     PAGES = {A3211--A3239},
       DOI = {10.1137/17M1149961},
       URL = {http://doi.org/10.1137/17M1149961}
}

@book {GuermondErn2004,
    AUTHOR = {A. Ern and J.-L. Guermond},
     TITLE = {Theory and practice of finite elements},
    SERIES = {Applied Mathematical Sciences},
    VOLUME = {159},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2004},
     PAGES = {xiv+524},
       DOI = {10.1007/978-1-4757-4355-5},
       URL = {https://doi.org/10.1007/978-1-4757-4355-5}
}

@article {Brooks1982,
    AUTHOR = {A.N. Brooks and T.J.R. Hughes},
     TITLE = {Streamline upwind/{P}etrov-{G}alerkin formulations for convection dominated flows with particular emphasis on the incompressible {N}avier-{S}tokes equations},
      NOTE = {FENOMECH ''81, Part I (Stuttgart, 1981)},
   JOURNAL = {Computer Methods in Applied Mechanics and Engineering},
      YEAR = {1982},
    VOLUME = {32},
    NUMBER = {1-3},
     PAGES = {199--259},
       DOI = {10.1016/0045-7825(82)90071-8},
       URL = {https://doi.org/10.1016/0045-7825(82)90071-8}
}

@article {Johnson1986,
    AUTHOR = {C. Johnson and J. Pitk\"{a}ranta},
     TITLE = {An analysis of the discontinuous {G}alerkin method for a scalar hyperbolic equation},
   JOURNAL = {Mathematics of Computation},
      YEAR = {1986},
    VOLUME = {46},
    NUMBER = {173},
     PAGES = {1--26},
       DOI = {10.2307/2008211},
       URL = {https://doi.org/10.2307/2008211}
}

@book{Rainald2008,
  author =    {R. Lohner},
  title =     {Edge-Based Compressible Flow Solvers},
  booktitle = {Applied Computational Fluid Dynamics Techniques},
  publisher = {John Wiley & Sons, Ltd},
  year =      {2008},
  chapter =   {10},
  pages =     {187-200},
  doi =       {10.1002/9780470989746.ch10},
  url =       {https://doi.org/10.1002/9780470989746.ch10}
}

@book {Toro2009,
  AUTHOR =    {F.T. Eleuterio},
  TITLE =     {Riemann Solvers and Numerical Methods for Fluid Dynamics},
  PUBLISHER = {Springer-Verlag, Berlin, Heidelberg},
  year =      {2009},
  doi =       {10.1007/b79761},
  url =       {https:doi.org/10.1007/b79761}
}


% ------------------------------------
% Step 70
% ------------------------------------


@inproceedings{Freund1995,
  author =    {J. Freund and R. Stenberg},
  title =     {On weakly imposed boundary conditions for second order problems},
  booktitle = {Proceedings of the Ninth International Conference on Finite Elements in Fluids},
  year =      {1995},
  pages =     {327--336}
}

@article{Angot1999,
  author =    {P. Angot and C.-H. Bruneau and P. Fabrie},
  title =     {A penalization method to take into account obstacles in incompressible viscous flows},
  journal =   {Numerische Mathematik},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {1999},
  month =     feb,
  volume =    {81},
  number =    {4},
  pages =     {497--520},
  doi =       {10.1007/s002110050401},
  url =       {https://doi.org/10.1007/s002110050401}
}

@article{Glowinski1999,
  author =    {R. Glowinski and T.-W. Pan and T.I. Hesla and D.D. Joseph},
  title =     {A distributed Lagrange multiplier/fictitious domain method for particulate flows},
  journal =   {International Journal of Multiphase Flow},
  publisher = {Elsevier BV},
  year =      {1999},
  month =     aug,
  volume =    {25},
  number =    {5},
  pages =     {755--794},
  doi =       {10.1016/s0301-9322(98)00048-2},
  url =       {https://doi.org/10.1016/s0301-9322(98)00048-2}
}

@article{Boffi2008,
  author =    {D. Boffi and L. Gastaldi and L. Heltai and Ch.S. Peskin},
  title =     {On the hyper-elastic formulation of the immersed boundary method},
  journal =   {Computer Methods in Applied Mechanics and Engineering},
  publisher = {Elsevier BV},
  year =      {2008},
  month =     apr,
  volume =    {197},
  number =    {25-28},
  pages =     {2210--2231},
  doi =       {10.1016/j.cma.2007.09.015},
  url =       {https://doi.org/10.1016/j.cma.2007.09.015}
}

@article{Heltai2012,
  author =    {L. Heltai and F. Costanzo},
  title =     {Variational implementation of immersed finite element methods},
  journal =   {Computer Methods in Applied Mechanics and Engineering},
  publisher = {Elsevier BV},
  year =      {2012},
  month =     jul,
  volume =    {229-232},
  pages =     {110--127},
  doi =       {10.1016/j.cma.2012.04.001},
  url =       {https://doi.org/10.1016/j.cma.2012.04.001}
}

@article{Riviere1999,
  author =    {B. Rivi{\`{e}}re and M.F. Wheeler and V. Girault},
  title =     {Improved energy estimates for interior penalty, constrained and discontinuous {G}alerkin methods for elliptic problems. {P}art {I}},
  journal =   {Computational Geosciences},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {1999},
  volume =    {3},
  number =    {3},
  pages =     {337--360},
  doi =       {10.1023/a:1011591328604},
  url =       {https://doi.org/10.1023/a:1011591328604}
}


% ------------------------------------
% Step 71
% ------------------------------------


@book{Pelteret2019a,
  author    = {J.-P. Pelteret and P. Steinmann},
  title     = {Magneto-active polymers: Fabrication, characterisation, modelling and simulation at the micro- and macro-scale},
  publisher = {De Gruyter Mouton},
  year      = {2019},
  edition   = {1},
  doi       = {10.1515/9783110418576},
  url       = {https://www.degruyter.com/document/doi/10.1515/9783110418576/html}
}

@book{Logg2012a,
  title     = {Automated Solution of Differential Equations by the Finite Element Method},
  publisher = {Springer Berlin Heidelberg},
  year      = {2012},
  editor    = {A. Logg and K.-A. Mardal and G. Wells},
  doi       = {10.1007/978-3-642-23099-8},
  url       = {https://doi.org/10.1007/978-3-642-23099-8}
}

@book{Korelc2016a,
  author    = {J. Korelc and P. Wriggers},
  title     = {Automation of Finite Element Methods},
  publisher = {Springer Nature},
  year      = {2016},
  doi       = {10.1007/978-3-319-39005-5},
  url       = {https://doi.org/10.1007/978-3-319-39005-5}
}

@inbook{Truesdell1960a,
  author    = {C. Truesdell and R. Toupin},
  title     = {Encyclopedia of Physics: Principles of Thermodynamics and Statics},
  chapter   = {2: The classical field theories},
  publisher = {Springer-Verlag Berlin Heidelberg},
  year      = {1960},
  editor    = {S. Fl\"{u}gge},
  volume    = {1},
  pages     = {226--794},
  doi       = {10.1007/978-3-642-45943-6},
  url       = {https://doi.org/10.1007/978-3-642-45943-6}
}

@article{Coleman1963a,
  author    = {B.D. Coleman and W. Noll},
  title     = {The thermodynamics of elastic materials with heat conduction and viscosity},
  journal   = {Archive for Rational Mechanics and Analysis},
  publisher = {Springer},
  year      = {1963},
  volume    = {13},
  number    = {1},
  pages     = {167--178},
  doi       = {10.1007/BF01262690},
  url       = {https://doi.org/10.1007/BF01262690}
}

@article{Coleman1967a,
  author    = {B.D. Coleman and M.E. Gurtin},
  title     = {Thermodynamics with internal state variables},
  journal   = {The Journal of Chemical Physics},
  publisher = {{AIP} Publishing},
  year      = {1967},
  volume    = {47},
  number    = {2},
  pages     = {597--613},
  doi       = {10.1063/1.1711937},
  url       = {https://doi.org/10.1063/1.1711937}
}

@incollection{Pao1978a,
  author    = {Y.H. Pao},
  title     = {Electromagnetic Forces in Deformable Continua},
  booktitle = {Mechanics Today},
  publisher = {Elsevier},
  year      = {1978},
  editor    = {S. Nemat-Nasser},
  volume    = {4},
  series    = {Pergamon Mechanics Today Series},
  chapter   = {IV},
  pages     = {209--305},
  address   = {New York},
  doi       = {10.1016/b978-0-08-021792-5.50012-4},
  url       = {https://doi.org/10.1016/b978-0-08-021792-5.50012-4}
}

@article{Holzapfel1996a,
  author    = {G.A. Holzapfel and J.C. Simo},
  title     = {A new viscoelastic constitutive model for continuous media at finite thermomechanical changes},
  journal   = {International Journal of Solids and Structures},
  publisher = {Elsevier},
  year      = {1996},
  month     = aug,
  volume    = {33},
  number    = {20--22},
  pages     = {3019--3034},
  doi       = {10.1016/0020-7683(95)00263-4},
  url       = {https://doi.org/10.1016/0020-7683(95)00263-4}
}

@book{Holzapfel2007a,
  author    = {G.A. Holzapfel},
  title     = {Nonlinear Solid Mechanics: A Continuum Approach for Engineering},
  publisher = {John Wiley \& Sons Ltd.},
  year      = {2007},
  address   = {West Sussex, England}
}

@article{Linder2011a,
  author    = {C. Linder and M. Tkachuk and C. Miehe},
  title     = {A micromechanically motivated diffusion-based transient network model and its incorporation into finite rubber viscoelasticity},
  journal   = {Journal of the Mechanics and Physics of Solids},
  publisher = {Elsevier},
  year      = {2011},
  month     = oct,
  volume    = {59},
  number    = {10},
  pages     = {2134--2156},
  url       = {https://doi.org/10.1016/j.jmps.2011.05.005}
}

@article{Pelteret2018a,
  author    = {J.-P. Pelteret and B. Walter and P. Steinmann},
  title     = {Application of metaheuristic algorithms to the identification of nonlinear magneto-viscoelastic constitutive parameters},
  journal   = {Journal of Magnetism and Magnetic Materials},
  publisher = {Elsevier BV},
  year      = {2018},
  volume    = {464},
  pages     = {116--131},
  doi       = {10.1016/j.jmmm.2018.02.094},
  url       = {https://doi.org/10.1016/j.jmmm.2018.02.094}
}

@article{Koprowski-Theiss2011a,
  author    = {N. Koprowski-Theiss and M. Johlitz and S. Diebels},
  title     = {Characterizing the time dependence of filled {EPDM}},
  journal   = {Rubber Chemistry and Technology},
  year      = {2011},
  month     = jun,
  volume    = {84},
  number    = {2},
  pages     = {147--165},
  doi       = {10.5254/1.3570527},
  url       = {https://doi.org/10.5254/1.3570527}
}


% ------------------------------------
% Step 74
% ------------------------------------

@book{di2011mathematical,
  author =    {D.A. Di Pietro and A. Ern},
  title =     {Mathematical aspects of discontinuous {G}alerkin methods},
  publisher = {Springer Science \& Business Media},
  volume =    {69},
  year =      {2011},
  url =       {https://doi.org/10.1007/978-3-642-22980-0}
}

@article{ainsworth2007posteriori,
  author =    {M. Ainsworth},
  title =     {A posteriori error estimation for discontinuous {G}alerkin finite element approximation},
  journal =   {SIAM Journal on Numerical Analysis},
  publisher = {SIAM},
  year =      {2007},
  volume =    {45},
  number =    {4},
  pages =     {1777--1798},
  url =       {https://doi.org/10.1137/060665993}
}


% ------------------------------------
% Step 75
% ------------------------------------

@book{brenner2008,
  author    = {S. Brenner and R. Scott},
  title     = {The {{Mathematical Theory}} of {{Finite Element Methods}}},
  publisher = {{Springer-Verlag}},
  year      = {2008},
  edition   = {3},
  series    = {Texts in {{Applied Mathematics}}},
  location  = {{New York}},
  url       = {https://www.springer.com/de/book/9780387759333}
}

@article{mitchell2010hpmg,
  author  = {W.F. Mitchell},
  title   = {The \textit{hp}‐multigrid method applied to \textit{hp}‐adaptive refinement of triangular grids},
  journal = {Numerical Linear Algebra with Applications},
  year    = {2010},
  month   = apr,
  volume  = {17},
  number  = {2-3},
  pages   = {211--228},
  url     = {https://doi.org/10.1002/nla.700}
}

@article{mitchell2014hp,
  author  = {W.F. Mitchell and M.A. McClain},
  title   = {A Comparison of \textit{hp}-Adaptive Strategies for Elliptic Partial Differential Equations},
  journal = {ACM Transactions on Mathematical Software},
  year    = {2014},
  volume  = {41},
  number  = {1},
  pages   = {2/1-39},
  doi     = {10.1145/2629459},
  url     = {https://doi.org/10.1145/2629459}
}


% ------------------------------------
% Step 76
% ------------------------------------

@misc{munch2020hyperdeal,
  author =        {P. Munch and K. Kormann and M. Kronbichler},
  title =         {hyper.deal: An efficient, matrix-free finite-element library for high-dimensional partial differential equations},
  year =          {2020},
  eprint =        {2002.08110},
  archivePrefix = {arXiv},
  primaryClass =  {cs.MS}
}


% ------------------------------------
% Step 77
% ------------------------------------


@article{eiwa96,
  author = {C.E. Stanley and F.W. Homer},
  title = {Choosing the Forcing Terms in an Inexact {N}ewton Method},
  journal = {SIAM Journal on Scientific Computing},
  year = {1996},
  volume = {17},
  number = {1},
  pages = {16--32},
  doi = {10.1137/0917003},
  URL = {https://doi.org/10.1137/0917003}
}


% ------------------------------------
% Step 78
% ------------------------------------

@article{black1973pricing,
  author =  {F. Black and M. Scholes},
  title =   {The Pricing of Options and Corporate Liabilities},
  journal = {The Journal of Political Economy},
  year =    {1973},
  volume =  {81},
  number =  {3},
  pages =   {637--654},
  url =     {https://doi.org/10.1086/260062}
}

@article{stoll1969relationship,
  author =    {H.R. Stoll},
  title =     {The relationship between put and call option prices},
  journal =   {The Journal of Finance},
  publisher = {Wiley Online Library},
  year =      {1969},
  volume =    {24},
  number =    {5},
  pages =     {801--824},
  url =       {https://doi.org/10.1111/j.1540-6261.1969.tb01694.x}
}


% ------------------------------------
% Step 79
% ------------------------------------

@book{Bendse2004,
  author =    {M.P. Bends{\o}e and O. Sigmund},
  title =     {Topology Optimization},
  publisher = {Springer Berlin Heidelberg},
  year =      {2004},
  doi =       {10.1007/978-3-662-05086-6},
  url =       {https://doi.org/10.1007/978-3-662-05086-6}
}

@book{Nocedal2006,
  author =    {J. Nocedal and S. Wright},
  title =     {Numerical Optimization},
  publisher = {Springer New York},
  year =      {2006},
  doi =       {10.1007/978-0-387-40065-5},
  url =       {https://doi.org/10.1007/978-0-387-40065-5}
}

@article{Waechter2005,
  author =    {A. W\"{a}chter and L.T. Biegler},
  title =     {On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming},
  journal =   {Mathematical Programming},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {2005},
  month =     apr,
  volume =    {106},
  number =    {1},
  pages =     {25--57},
  doi =       {10.1007/s10107-004-0559-y},
  url =       {https://doi.org/10.1007/s10107-004-0559-y}
}

@article{Nocedal2009,
  author =    {J. Nocedal and A. W\"{a}chter and R.A. Waltz},
  title =     {Adaptive Barrier Update Strategies for Nonlinear Interior Methods},
  journal =   {SIAM Journal on Optimization},
  publisher = {Society for Industrial {\&} Applied Mathematics (SIAM)},
  year =      {2009},
  month =     jan,
  volume =    {19},
  number =    {4},
  pages =     {1674--1693},
  doi =       {10.1137/060649513},
  url =       {https://doi.org/10.1137/060649513}
}

@article{Benson2002,
  author =    {H.Y. Benson and R.J. Vanderbei and D.F. Shanno},
  title =     {Interior-Point Methods for Nonconvex Nonlinear Programs: Filter Methods and Merit Functions},
  journal =   {Computational Optimization and Applications},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {2002},
  volume =    {23},
  number =    {2},
  pages =     {257--272},
  doi =       {10.1023/a:1020533003783},
  url =       {https://doi.org/10.1023/a:1020533003783}
}

% ------------------------------------
% Step 81
% ------------------------------------

@BOOK{Schwartz1972,
  AUTHOR={M. Schwartz},
  TITLE={Principles of Electrodynamics},
  Year={1972},
  PUBLISHER={McGraw-Hill Book Company},
  ADDRESS={New York},
  SERIES={International Series in Pure and Applied Physics},
}

@ARTICLE{berenger1994,
  AUTHOR={Jean-Pierre Bérenger},
  TITLE={A Perfectly Matched Layer for the Absorption of Electromagnetic
    Waves},
  JOURNAL={Journal of Computational Physics},
  VOLUME={114},
  PAGES={185-200},
  YEAR={1994},
}

@ARTICLE{Gopalakrishnan2003,
  AUTHOR={J. Gopalakrishnan and Pasciak, J. E.},
  TITLE={Overlapping Schwarz preconditioners for indefinite time harmonic
    {M}axwell equations},
  JOURNAL={Math. Comput.},
  VOLUME={72},
  PAGES={1-15},
  YEAR={2003}
}

@BOOK{Monk2003,
  AUTHOR={P. Monk},
  TITLE={Finite Element Methods for {Maxwell's} Equations},
  YEAR={2003},
  PUBLISHER={Oxford University Press},
  SERIES={Numerical Mathematics and Scientific Computation},
}

@ARTICLE{Geim2004,
  AUTHOR={K.S. Novoselov and A.K. Geim and S.V. Morozov and D. Jiang and Y. Zhang and S.V. Dubonos and I.V. Grigorieva and A.A. Firsov},
  TITLE={Electric Field Effect in Atomically Thin Carbon Films},
  JOURNAL={Science},
  VOLUME={306},
  PAGES={666},
  YEAR={2004}
}

@ARTICLE{Maier2017,
    author = {M. Maier and D. Margetis and M. Luskin},
    journal = {Journal of Computational Physics},
    pages = {126--145},
    title = {Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation},
    volume = {339},
    year = {2017}
}

@ARTICLE{Ying2012,
  TITLE={A sweeping preconditioner for time-harmonic {M}axwell's equations},
  AUTHOR={P. Tsuji and B. Engquist and L. Ying},
  YEAR={2012},
  JOURNAL={J. Comput. Phys.},
  VOLUME={231},
  PAGES={3770-3783},
}


% ------------------------------------
% Step 82
% ------------------------------------

@article{Pryer2014,
 author = {T. Pryer},
 title = {Discontinuous {G}alerkin methods for the p-biharmonic equation from a discrete variational perspective},
 journal = {Electronic Transactions of Numerical Analysis},
 volume = {41},
 pages = {328--349},
 year = {2014}
}

@article{Bonito2021,
  author = {A. Bonito and R.H. Nochetto and D. Ntogkas},
  title = {{DG} Approach to Large Bending Plate Deformations with Isometry Constraint},
  journal = {Mathematical Models and Methods in Applied Sciences},
  volume = {31},
  number = {1},
  pages = {133--175},
  year = {2021}
}

@book{DiPietro2011,
  author = {D.A. Di Pietro and A. Ern},
  title = {Mathematical Aspects of Discontinuous {G}alerkin Methods},
  series = {Math{\'e}matiques et Applications},
  publisher={Springer Berlin Heidelberg},
  year={2011},
}

@article{BGNY2020,
  title={{LDG} approximation of large deformations of prestrained plates},
  author={A. Bonito and D. Guignard and R.H. Nochetto and S. Yang},
  journal={To appear in Journal of Computational Physics},
  year={2021},
  url = {https://doi.org/10.1016/j.jcp.2021.110719}
}

@article{BGNY2021,
  title={Numerical analysis of the {LDG} method for large deformations of prestrained plates},
  author={A. Bonito and D. Guignard and R.H. Nochetto and S. Yang},
  journal={Submitted},
  year={2021},
  url = {https://arxiv.org/abs/2106.13877}
}

% ------------------------------------
% Step 85
% ------------------------------------

@article{saye_2015,
	title = {High-{Order} {Quadrature} {Methods} for {Implicitly} {Defined} {Surfaces} and {Volumes} in {Hyperrectangles}},
	volume = {37},
	issn = {1064-8275, 1095-7197},
	url = {http://epubs.siam.org/doi/10.1137/140966290},
	doi = {10.1137/140966290},
	language = {en},
	number = {2},
	urldate = {2016-01-27},
	journal = {SIAM Journal on Scientific Computing},
	author = {Saye, R. I.},
	month = jan,
	year = {2015},
	pages = {A993--A1019}
}

@article{burman_hansbo_2012,
	title = {Fictitious domain finite element methods using cut elements: {II}. {A} stabilized {Nitsche} method},
	volume = {62},
	issn = {01689274},
	url = {http://linkinghub.elsevier.com/retrieve/pii/S0168927411000298},
	doi = {10.1016/j.apnum.2011.01.008},
	language = {en},
	number = {4},
	urldate = {2015-12-17},
	journal = {Applied Numerical Mathematics},
	author = {Burman, Erik and Hansbo, Peter},
	month = apr,
	year = {2012},
	pages = {328--341}
}

@article{cutfem_2015,
	title = {{CutFEM}: {Discretizing} geometry and partial differential equations},
	volume = {104},
	issn = {00295981},
	url = {http://doi.wiley.com/10.1002/nme.4823},
	doi = {10.1002/nme.4823},
	language = {en},
	number = {7},
	urldate = {2016-01-27},
	journal = {International Journal for Numerical Methods in Engineering},
	author = {Burman, Erik and Claus, Susanne and Hansbo, Peter and Larson, Mats G. and Massing, André},
	month = nov,
	year = {2015},
	pages = {472--501}
}


% ------------------------------------
% References used elsewhere
% ------------------------------------

@article{KGZB83,
  author  = {D.W. Kelly and J.P. De S. R. Gago and O.C. Zienkiewicz and I. Babu\v{s}ka},
  title   = {A posteriori error analysis and adaptive processes in the finite element method: Part {I}--Error Analysis},
  journal = {International Journal for Numerical Methods in Engineering},
  year    = {1983},
  volume  = {19},
  pages   = {1593--1619},
  url     = {https://doi.org/10.1002/nme.1620191103}
}

@article{park2003p,
   author    = {C. Park and D. Sheen},
   title     = {P1-nonconforming quadrilateral finite element methods for second-order elliptic problems},
   journal   = {SIAM Journal on Numerical Analysis},
   publisher = {SIAM},
   year      = {2003},
   volume    = {41},
   number    = {2},
   pages     = {624--640},
   doi       = {10.1137/S0036142902404923},
   url       = {https://doi.org/10.1137/S0036142902404923}
}

@article{GLHPW2018,
  author =    {R. Gassm\"{o}ller and H. Lokavarapu and E. Heien and E.G. Puckett and W. Bangerth},
  title =     {Flexible and Scalable Particle-in-Cell Methods With Adaptive Mesh Refinement for Geodynamic Computations},
  journal =   {Geochemistry,  Geophysics,  Geosystems},
  publisher = {American Geophysical Union (AGU)},
  year =      {2018},
  volume =    {19},
  number =    {9},
  pages =     {3596--3604},
  doi =       {10.1029/2018gc007508},
  url =       {https://doi.org/10.1029/2018gc007508}
}

@techreport{Saad1991,
  Author                   = {Y. Saad},
  Title                    = {{A Flexible Inner-Outer Preconditioned {GMRES} Algorithm}},
  Institution              = {Minnesota Supercomputer Institute},
  Year                     = {1991},
  Address                  = {University of Minnesota},
  Number                   = {91-279},
  Url                      = {citeseer.ist.psu.edu/saad93flexible.html}
}

@article{ainsworth1998hp,
  author    = {M. Ainsworth and B. Senior},
  title     = {An adaptive refinement strategy for \textit{hp}-finite element computations},
  journal   = {Applied Numerical Mathematics},
  publisher = {Elsevier},
  year      = {1998},
  volume    = {26},
  number    = {1--2},
  pages     = {165--178},
  doi       = {10.1016/S0168-9274(97)00083-4},
  url       = {https://doi.org/10.1016/S0168-9274(97)00083-4}
}

@article{melenk2001hp,
  author    = {J.M. Melenk and B.I. Wohlmuth},
  title     = {On residual-based a posteriori error estimation in \textit{hp}-{FEM}},
  journal   = {Advances in Computational Mathematics},
  publisher = {Springer US},
  year      = {2001},
  volume    = {15},
  number    = {1},
  pages     = {311--331},
  doi       = {10.1023/A:1014268310921},
  url       = {https://doi.org/10.1023/A:1014268310921}
}

@article{mavriplis1994hp,
  author    = {C. Mavriplis},
  title     = {Adaptive mesh strategies for the spectral element method},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  publisher = {Elsevier},
  year      = {1994},
  volume    = {116},
  number    = {1},
  pages     = {77--86},
  url       = {https://doi.org/10.1016/S0045-7825(94)80010-3}
}

@article{houston2005hp,
  author    = {P. Houston and E. S{\"u}li},
  title     = {A note on the design of \textit{hp}-adaptive finite element methods for elliptic partial differential equations},
  journal   = {Computer Methods in Applied Mechanics and Engineering},
  publisher = {Elsevier},
  year      = {2005},
  number    = {2},
  volume    = {194},
  pages     = {229--243},
  doi       = {10.1016/j.cma.2004.04.009},
  url       = {https://doi.org/10.1016/j.cma.2004.04.009}
}

@article{eibner2007hp,
  author    = {T. Eibner and J.M. Melenk},
  title     = {An adaptive strategy for \textit{hp}-{FEM} based on testing for analyticity},
  journal   = {Computational Mechanics},
  publisher = {Springer},
  year      = {2007},
  volume    = {39},
  number    = {5},
  pages     = {575--595},
  doi       = {10.1007/s00466-006-0107-0},
  url       = {https://doi.org/10.1007/s00466-006-0107-0}
}

@article{davydov2017hp,
  author  = {D. Davydov and T. Gerasimov and J.-P. Pelteret and P. Steinmann},
  title   = {Convergence study of the \textit{h}-adaptive {PUM} and the \textit{hp}-adaptive {FEM} applied to eigenvalue problems in quantum mechanics},
  journal = {Advanced Modeling and Simulation in Engineering Sciences},
  year    = {2017},
  volume  = {4},
  number  = {1},
  pages   = {7},
  url     = {https://doi.org/10.1186/s40323-017-0093-0}
}

@article{clevenger_par_gmg,
  author = {T.C. Clevenger and T. Heister and G. Kanschat and M. Kronbichler},
  title = {A Flexible, Parallel, Adaptive Geometric Multigrid Method for {FEM}},
  year = {2021},
  month = mar,
  publisher = {Association for Computing Machinery ({ACM})},
  volume = {47},
  number = {1},
  pages = {1--27},
  journal = {{ACM} Transactions on Mathematical Software},
  doi = {10.1145/3425193},
  url = {https://doi.org/10.1145/3425193}
}

@book{CodeComplete,
  author =    {S. McConnell},
  title =     {Code Complete},
  publisher = {Microsoft Press},
  year =      {2004},
  edition =   {second}
}

@article{gottlieb2001strong,
  author =    {S. Gottlieb and C.-W. Shu and E. Tadmor},
  title =     {Strong stability-preserving high-order time discretization methods},
  journal =   {SIAM review},
  publisher = {SIAM},
  year =      {2001},
  volume =    {43},
  number =    {1},
  pages =     {89--112},
  url =       {https://doi.org/10.1137/S003614450036757X}
}

@article{melenk1996,
  author  = {J.M. Melenk and I. Babu\v{s}ka},
  title   = {The partition of unity finite element method: Basic theory and applications},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year    = {1996},
  number  = {1--4},
  volume  = {139},
  pages   = {289--314},
  doi     = {10.1016/S0045-7825(96)01087-0},
  url     = {https://doi.org/10.1016/S0045-7825(96)01087-0}
}

@article{babuska1997,
  author  = {I. Babu\v{s}ka and J.M. Melenk},
  title   = {The partition of unity method},
  journal = {International Journal for Numerical Methods in Engineering},
  year    = {1997},
  number  = {4},
  volume  = {40},
  pages   = {727--758},
  doi     = {10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N},
  url     = {https://doi.org/10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N}
}

@article{Bartels2004,
  author =    {S. Bartels and C. Carstensen and G. Dolzmann},
  title =     {Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis},
  journal =   {Numerische Mathematik},
  publisher = {Springer Science and Business Media {LLC}},
  year =      {2004},
  month =     sep,
  volume =    {99},
  number =    {1},
  pages =     {1--24},
  doi =       {10.1007/s00211-004-0548-3},
  url =       {https://doi.org/10.1007/s00211-004-0548-3}
}

@article{fried1975finite,
  author =    {I. Fried and D.S. Malkus},
  title =     {Finite element mass matrix lumping by numerical integration with no convergence rate loss},
  journal =   {International Journal of Solids and Structures},
  publisher = {Elsevier},
  year =      {1975},
  volume =    {11},
  number =    {4},
  pages =     {461--466},
  url =       {https://doi.org/10.1016/0020-7683(75)90081-5}
}

@article{Geevers_2018,
   author =    {S. Geevers and W.A. Mulder and J.J.W. van der Vegt},
   title =     {New Higher-Order Mass-Lumped Tetrahedral Elements for Wave Propagation Modelling},
   journal =   {SIAM Journal on Scientific Computing},
   publisher = {Society for Industrial & Applied Mathematics (SIAM)},
   year =      {2018},
   number =    {5},
   volume =    {40},
   pages =     {A2830--A2857},
   doi =       {10.1137/18m1175549},
   url =       {https://doi.org/10.1137/18m1175549}
}

@article{witherden2015identification,
  author =    {F.D. Witherden and P.E. Vincent},
  title =     {On the identification of symmetric quadrature rules for finite element methods},
  journal =   {Computers \& Mathematics with Applications},
  publisher = {Elsevier},
  year =      {2015},
  volume =    {69},
  number =    {10},
  pages =     {1232--1241},
  url =       {https://doi.org/10.1016/j.camwa.2015.03.017}
}

@online{quadpy,
  author =  {N. Schl{\"o}mer},
  title =   {quadpy: Your one-stop shop for numerical integration in {P}ython},
  year =    {2021},
  url =     {https://github.com/nschloe/quadpy/},
  urldate = {2021-02-08}
}

@Article{AABB17,
  author =  {R. Agelek and M. Anderson and W. Bangerth and W.L. Barth},
  title =   {On orienting edges of unstructured two- and three-dimensional meshes},
  journal = {ACM Transactions on Mathematical Software},
  year =    {2017},
  volume =  {44},
  number =  {1},
  pages =   {5/1--22},
  url =     {https://doi.org/10.1145/3061708}
}

@article{hoefler2010scalable,
  author =    {T. Hoefler and C. Siebert and A. Lumsdaine},
  title =     {Scalable communication protocols for dynamic sparse data exchange},
  journal =   {ACM Sigplan Notices},
  publisher = {ACM New York, NY, USA},
  year =      {2010},
  volume =    {45},
  number =    {5},
  pages =     {159--168},
  url =       {https://doi.org/10.1145/1837853.1693476}
}

@inproceedings{ljungkvist2017matrix,
  title={Matrix-free finite-element computations on graphics processors with adaptively refined unstructured meshes},
  author={K. Ljungkvist},
  booktitle={Proceedings of the 25th High Performance Computing Symposium},
  series={HPC '17},
  articleno={1},
  numpages={12},
  year={2017},
  url={https://dl.acm.org/doi/10.5555/3108096.3108097}
}

@article{kronbichler2019multigrid,
  title={Multigrid for matrix-free high-order finite element computations on graphics processors},
  author={M. Kronbichler and K. Ljungkvist},
  journal={ACM Transactions on Parallel Computing (TOPC)},
  volume={6},
  number={1},
  pages={1--32},
  year={2019},
  publisher={ACM New York, NY, USA},
  doi={10.1145/3322813},
  url={https://doi.org/10.1145/3322813}
}

@article{Boffi2011,
  doi = {10.1007/s10915-011-9549-4},
  url = {https://doi.org/10.1007/s10915-011-9549-4},
  year = {2011},
  month = nov,
  publisher = {Springer Science and Business Media {LLC}},
  volume = {52},
  number = {2},
  pages = {383--400},
  author = {D. Boffi and N. Cavallini and F. Gardini and L. Gastaldi},
  title = {Local Mass Conservation of Stokes Finite Elements},
  journal = {Journal of Scientific Computing}
}

@article{Taylor73,
title={{A numerical solution of the Navier-Stokes equations using the finite element technique}},
author={C. Taylor and P. Hood},
journal={Comput. Fluids},
volume={1},
number={1},
pages={73--100},
year={1973},
doi = {10.1016/0045-7930(73)90027-3},
url = {https://doi.org/10.1016/0045-7930(73)90027-3}
}

@article{Bercovier1979,
  doi = {10.1007/bf01399555},
  url = {https://doi.org/10.1007/bf01399555},
  year = {1979},
  month = jun,
  publisher = {Springer Science and Business Media {LLC}},
  volume = {33},
  number = {2},
  pages = {211--224},
  author = {M. Bercovier and O. Pironneau},
  title = {Error estimates for finite element method solution of the {S}tokes problem in the primitive variables},
  journal = {Numerische Mathematik}
}

@MastersThesis{Battermann1996,
  author    = {A. Battermann},
  title     = {Preconditioning of Karush--Kuhn--Tucker Systems arising in Optimal Control Problems},
  school    = {Virginia Tech},
  year      = {1996},
  month     = jun,
  url       = {http://hdl.handle.net/10919/9579}
}

@article{Boffi2012,
  author = {D. Boffi and N. Cavallini and F. Gardini and L. Gastaldi},
  title = {Local Mass Conservation of Stokes Finite Elements},
  journal = {Journal of Scientific Computing},
  year = {2012},
  volume = {52},
  issue = {2},
  pages = {383--400},
  doi = {10.1007/s10915-011-9549-4},
  url = {http://doi.org/10.1007/s10915-011-9549-4}
}

@PhDThesis{Richter2005,
  author = {T. Richter},
  title  = {Parallel Multigrid Method for Adaptive Finite Elements with Application to 3D Flow Problems},
  school = {Universit{\"a}t Heidelberg},
  year   = {2005},
  doi    = {10.11588/heidok.00005743},
  url    = {https://doi.org/10.11588/heidok.00005743}
}

@article{Chronopoulos1989,
  author = {A. T. Chronopoulos and C. W. Gear},
  title = {S-step Iterative Methods for Symmetric Linear Systems},
  journal = {Journal of Computational and Applied Mathematics},
  volume = {25},
  number = {2},
  year = {1989},
  pages = {153--168},
  url = {https://doi.org/10.1016/0377-0427(89)90045-9}
}
