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

@article{Mu05,
  author =  {Mo Mu},
  title =   {{PDE.M}art: A Network-based Problem-solving Environment for {PDE}s},
  journal = {ACM Trans. Math. Software.},
  year =    2005,
  volume =  31,
  number =  4,
  pages =   {508--531}
}

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

@article{Kel74,
  author =  {R. Bruce Kellogg},
  title =   {On the {P}oisson equation with intersecting interfaces},
  journal = {Applicable Analysis},
  year  =   1974,
  volume =  4,
  number =  2,
  pages =   {101--129}
}

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

@inproceedings{Ban00w,
  author =  {Wolfgang 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},
  year =    2000,
  editor =  {Alfredo Berm\'udez and Dolores G\'omez and Christophe Hazard and
             Patrick Joly and Jean E. Roberts},
  publisher =   {SIAM},
  pages =   {725--729}
}

@phdthesis{Ban02,
  author =  {Wolfgang Bangerth},
  title =   {Adaptive Finite Element Methods for the Identification
             of Distributed Parameters in Partial Differential Equations},
  school =  {University of Heidelberg},
  year =    2002
}

@article{BR99b,
  author =  {Wolfgang Bangerth and Rolf Rannacher},
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             control and mesh adaptation},
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  year =    1999,
  volume =  7,
  number =  4,
  pages =   {263--282}
}

@book{BR03,
  author =  {Wolfgang Bangerth and Rolf Rannacher},
  title =   {Adaptive Finite Element Methods for Differential Equations},
  publisher =   {Birkh{\"a}user Verlag},
  year =    2003
}

@article{BR01a,
  author =  {Wolfgang Bangerth and Rolf Rannacher},
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  volume =  9,
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}

@article{BR01,
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  volume =  10,
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}

@phdthesis{Bec95,
  author =  {Roland Becker},
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             {N}avier-{S}tokes Equations on Time-dependent Domains},
  school =  {Universit{\"a}t Heidelberg},
  type =    {Dissertation},
  year =    1995
}

@techreport{Bec98,
  author =  {Roland Becker},
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  type =    {Preprint 98-20},
  year =    1998
}

@article{BR96r,
  author =  {Roland Becker and Rolf Rannacher},
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  year =    1996,
  pages =   {237--264}
}

@inproceedings{BR95,
  author =  {Roland Becker and Rolf Rannacher},
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  booktitle =   {ENUMATH 97},
  editor =  {H. G. Bock et al.},
  publisher =   {World Scientific Publ., Singapore},
  year =    1998,
  pages =   {621--637}
}

@article{FK97,
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  number =  4,
  pages =   {317--334}
}

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

@article{HH01,
  author =  {Ralf Hartmann and Paul Houston},
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  publisher =   {SIAM}
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}

@article{HH01b,
  author =  {Ralf Hartmann and Paul Houston},
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             Compressible {E}uler Equations},
  journal = {Journal of Computational Physics},
  year =    2002,
  volume =  183,
  number =  2,
  pages =   {508--532}
}

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

@article{RS97,
  author =  {Rolf Rannacher and Franz-Theo Suttmeier},
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             Application to linear elasticity},
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  year =    1997,
  volume =  19,
  number =  5,
  pages =   {434--446}
}

@article{RS98c,
  author =  {Rolf Rannacher and Franz-Theo Suttmeier},
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  journal = {Computational Mechanics},
  year =    1998,
  volume =  21,
  number =  2,
  pages =   {123--133}
}

@article{RS99,
  author =  {Rolf Rannacher and Franz-Theo Suttmeier},
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             element models in elasto-plasticity},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    1999,
  volume =  176,
  number =  1,
  pages =   {333--361}
}

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


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

@article{CTZ04,
  author =  {Stéphane Commend and Andrzej Truty and Thomas Zimmermann},
  title =   {Stabilized finite elements applied to elastoplasticity: I. Mixed displacement–pressure formulation},
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  year =    2004,
  volume =  193,
  number =  33,
  pages =   {3559--3586}
}

@article{DL05,
  author =  {Huo-Yuan Duan and Qun Lin},
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  journal = {Computer Methods in Applied Mechanics and Engineering},
  year =    2005,
  volume =  194,
  number =  9,
  pages =   {1093--1112}
}


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

@article{Brenner2005,
  doi = {10.1007/s10915-004-4135-7},
  url = {https://doi.org/10.1007/s10915-004-4135-7},
  year = {2005},
  month = jun,
  publisher = {Springer Science and Business Media {LLC}},
  volume = {22-23},
  number = {1-3},
  pages = {83--118},
  author = {Susanne C. Brenner and Li-Yeng Sung},
  title = {$C^0$ Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains},
  journal = {Journal of Scientific Computing}
}


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

@article{Engel2002,
  doi = {10.1016/s0045-7825(02)00286-4},
  url = {https://doi.org/10.1016/s0045-7825(02)00286-4},
  year = {2002},
  month = jul,
  publisher = {Elsevier {BV}},
  volume = {191},
  number = {34},
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  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}
}

@article{Brenner2009,
  doi = {10.1093/imanum/drn057},
  url = {https://doi.org/10.1093/imanum/drn057},
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  publisher = {Oxford University Press ({OUP})},
  volume = {30},
  number = {3},
  pages = {777--798},
  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}
}

@article{Wells2007,
  doi = {10.1016/j.cma.2007.03.008},
  url = {https://doi.org/10.1016/j.cma.2007.03.008},
  year = {2007},
  month = jul,
  publisher = {Elsevier {BV}},
  volume = {196},
  number = {35-36},
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  author = {Garth N. Wells and Nguyen Tien Dung},
  title = {A C0 discontinuous Galerkin formulation for Kirchhoff plates},
  journal = {Computer Methods in Applied Mechanics and Engineering}
}

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

@article{karakashian2003posteriori,
  title={A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems},
  author={Karakashian, Ohannes A and Pascal, Frederic},
  journal={SIAM Journal on Numerical Analysis},
  volume={41},
  number={6},
  pages={2374--2399},
  year={2003},
  publisher={SIAM}
}

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

@article {Ngu2012,
    AUTHOR = {Nguyen, N. C. and Peraire, J.},
     TITLE = {Hybridizable discontinuous {G}alerkin methods for partial
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      ISSN = {0021-9991},
   MRCLASS = {65N30},
  MRNUMBER = {2954837},
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       URL = {https://doi.org/10.1016/j.jcp.2012.02.033},
}

@incollection{F65,
  author = {Fraeijs de Veubeke, B. X.},
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  year = {1965},
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}

@article{G65,
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@article {CGL2009,
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   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
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      YEAR = {2009},
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MRREVIEWER = {Jose Luis Gracia},
       DOI = {10.1137/070706616},
       URL = {http://dx.doi.org/10.1137/070706616},
}

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

@Book{elman2005,
  Title                    = {Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics},
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  Publisher                = {Oxford University Press},
  Year                     = {2005},
  Address                  = {Oxford, New York},
  Series                   = {Numerical Mathematics and Scientific Computation},
  ISBN                     = {0-19-852868-X},
}

@inproceedings{kovasznay1948laminar,
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  year={1948},
  organization={Cambridge University Press}
}


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

@incollection{Wang2019,
  doi = {10.1007/978-3-030-22747-0_37},
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  title = {deal.{II} Implementation of a Weak Galerkin Finite Element Solver for Darcy Flow},
  booktitle = {Lecture Notes in Computer Science}
}

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

@incollection{john2006discontinuity,
  title={On discontinuity—capturing methods for convection—diffusion equations},
  author={John, Volker and Knobloch, Petr},
  booktitle={Numerical Mathematics and Advanced Applications},
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@article{KanschatNotesIterative,
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}

@book{smith2004domain,
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@book{toselli2006domain,
  title={Domain decomposition methods-algorithms and theory},
  author={Toselli, Andrea and Widlund, Olof},
  volume={34},
  year={2006},
  publisher={Springer Science \& Business Media}
}

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

@article{KennedyCarpenterLewis2000,
author = {Kennedy, Christopher A. and Carpenter, Mark H. and Lewis, R. Micheal},
title = {Low-storage, explicit {R}unge--{K}utta schemes for the compressible {N}avier--{S}tokes equations},
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volume = 35,
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}

@article{TseliosSimos2007,
author = {Tselios, Kostas and Simos, Theodore E.},
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}

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

@article{SchoederKormann2018,
  title={Efficient explicit time stepping of high order discontinuous {G}alerkin schemes for waves},
  author={Schoeder, Svenja and Kormann, Katharina and Wall, Wolfgang A. and  Kronbichler, Martin},
  journal={SIAM J. Sci. Comput.},
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  volume = 40,
  number = 6,
  year={2018},
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  url={https://doi.org/10.1137/18M1185399}
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@article{FehnWallKronbichler2019,
author = {Fehn, Niklas and Wall, Wolfgang A. and Kronbichler, Martin},
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},
volume = {89},
number = {3},
pages = {71--102},
year = {2019},
doi = {10.1002/fld.4683},
url = {https://doi.org/10.1002/fld.4683}
}

@article{KronbichlerKormann2019,
author = {Kronbichler, Martin and Kormann, Katharina},
title  = {Fast matrix-free evaluation of discontinuous {G}alerkin finite element operators},
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number = {3},
pages = {29:1--29:40},
year = {2019},
doi = {10.1145/3325864},
url = {https://doi.org/10.1145/3325864}
}

@article{Gassner2013,
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  author = {Gregor 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}
}


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

@article {GuermondPopov2016,
    AUTHOR = {Guermond, Jean-Luc and Popov, Bojan},
     TITLE = {Invariant domains and first-order continuous finite element
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   JOURNAL = {SIAM J. Numer. Anal.},
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      ISSN = {0036-1429},
       DOI = {10.1137/16M1074291},
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@article {GuermondPopov2016b,
    AUTHOR = {Guermond, Jean-Luc and Popov, Bojan},
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@article {GuermondEtAl2018,
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@book {GuermondErn2004,
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 PUBLISHER = {Springer-Verlag, New York},
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@article {Brooks1982,
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      NOTE = {FENOMECH ''81, Part I (Stuttgart, 1981)},
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@article {Johnson1986,
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@book{Rainald2008,
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@book {Toro2009,
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  doi = {10.1007/b79761},
  year = {2009}
}


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

@article{Riviere1999,
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}

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  author    = {Ainsworth, Mark and Senior, Bill},
  title     = {An adaptive refinement strategy for hp-finite element computations},
  journal   = {{Applied Numerical Mathematics}},
  volume    = {26},
  number    = {1--2},
  pages     = {165--178},
  publisher = {Elsevier},
  year      = {1998},
  doi       = {10.1016/S0168-9274(97)00083-4}
}

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

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

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

@article{eibner2007hp,
  author    = {Eibner, Tino and Melenk, Jens Markus},
  title     = {{An adaptive strategy for hp-FEM based on testing for analyticity}},
  journal   = {{Computational Mechanics}},
  year      = {2007},
  volume    = {39},
  number    = {5},
  pages     = {575--595},
  publisher = {Springer},
  doi       = {10.1007/s00466-006-0107-0}
}

@article{davydov2017hp,
  author  = {Davydov, Denis and Gerasimov, Tymofiy and Pelteret, Jean-Paul and Steinmann, Paul},
  title   = {{Convergence study of the h-adaptive PUM and the 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},
  issn    = {2213-7467},
  doi     = {10.1186/s40323-017-0093-0}
}

@Article{clevenger_par_gmg,
  Title                    = {A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM},
  Author                   = {Thomas C. Clevenger and Timo Heister and Guido Kanschat and Martin Kronbichler},
  Journal                  = {submitted},
  Year                     = {2019},
  Url                      = {https://arxiv.org/abs/1904.03317}
}

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

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