@article{fiat,
       AUTHOR = {Robert C. Kirby},
        TITLE = {Algorithm 839: {FIAT}, a New Paradigm for Computing Finite Element Basis Functions},
         YEAR = {2004},
       VOLUME = {30},
       NUMBER = {4},
          DOI = {10.1145/1039813.1039820},
      JOURNAL = {ACM Transactions on Mathematical Software},
        PAGES = {{502--516}},
}

@article{fenics,
        TITLE = {The FEniCS Project Version 1.5},
        AUTHOR = {Martin S. Aln{\ae}s and Jan Blechta and Johan Hake and
        August Johansson and Benjamin Kehlet and Anders Logg and Chris
        N. Richardson and Johannes Ring and Marie E. Rognes and Garth N.
        Wells},
         YEAR = {2015},
      JOURNAL = {Archive of Numerical Software},
       VOLUME = {3},
       NUMBER = {100},
          DOI = {10.11588/ans.2015.100.20553},
        PAGES = {{9--23}},
}

@unpublished{dof-transformations,
     AUTHOR = {Matthew W. Scroggs and J{\o}rgen S. Dokken and Chris N. Richardson and Garth N. Wells},
      TITLE = {Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes},
       YEAR = {2021},
       NOTE = {to appear in ACM Transactions on Mathematical Software},
        DOI = {10.1145/3524456}
}

@article{ufl,
       AUTHOR = {Martin S. Aln{\ae}s and Anders Logg and Kristian B. {\O}lgaard and Marie E. Rognes and Garth N. Wells},
        TITLE = {{U}nified {F}orm {L}anguage: A domain-specific language for weak formulations of partial differential equations},
      JOURNAL = {{ACM} Transactions on Mathematical Software},
        ISSUE = {40},
         YEAR = {2014},
          DOI = {10.1145/2566630}
}

@book{ciarlet,
        TITLE = {The Finite Element Method for Elliptic Problems},
       AUTHOR = {Philippe G. Ciarlet},
         YEAR = {1978},
    PUBLISHER = {North-Holland},
}

@article{nedelec1,
       AUTHOR = {Jean-Claude {N}\'ed\'elec},
        TITLE = {{M}ixed finite elements in $\mathbb{{R}}^3$},
      JOURNAL = {Numerische Mathematik},
       VOLUME = {35},
       NUMBER = {3},
         YEAR = {1980},
          DOI = {10.1007/BF01396415},
        PAGES = {{315--341}},
}

@article{nedelec2,
       AUTHOR = {Jean-Claude {N}\'ed\'elec},
        TITLE = {{A} new family of mixed finite elements in \(\mathbb{{R}}^3\)},
      JOURNAL = {Numerische Mathematik},
       VOLUME = {50},
       NUMBER = {1},
         YEAR = {1986},
          DOI = {10.1007/BF01389668},
        PAGES = {{57--81}},
}

@incollection{rt,
       AUTHOR = {Pierre-Arnau {R}aviart and J.-M. {T}homas},
       EDITOR = {{G}alligani, {I}. and {M}agenes, {E}.},
        TITLE = {{A} mixed finite element method for 2nd order elliptic problems},
    BOOKTITLE = {{M}athematical aspects of finite element methods},
       VOLUME = {606},
         YEAR = {1977},
        PAGES = {{292--315}},
}

@article{bdm,
       AUTHOR = {Franco {B}rezzi and Jim {D}ouglas and L. D. {M}arini},
        TITLE = {{T}wo families of mixed finite elements for second order elliptic problems},
      JOURNAL = {Numerische Mathematik},
       VOLUME = {47},
         YEAR = {1985},
          DOI = {10.1007/BF01389710},
        PAGES = {{217--235}},
}

@article{cr,
       AUTHOR = {M. {C}rouzeix and Pierre-Arnau {R}aviart},
        TITLE = {{C}onforming and nonconforming finite element methods for solving the stationary {S}tokes equations},
      JOURNAL = {Revue Fran\c{c}aise d'Automatique, Informatique et Recherche Op\'erationnelle},
       VOLUME = {3},
         YEAR = {1973},
          DOI = {10.1051/m2an/197307R300331},
        PAGES = {{33--75}},
}

@article{regge,
       AUTHOR = {T. {R}egge},
        TITLE = {{G}eneral relativity without coordinates},
      JOURNAL = {Il Nuovo Cimento},
       VOLUME = {19},
       NUMBER = {3},
         YEAR = {1961},
          DOI = {10.1007/BF02733251},
        PAGES = {{558--571}},
}

@article{regge2,
       AUTHOR = {Snorre H. {C}hristiansen},
        TITLE = {{O}n the linearization of {R}egge calculus},
      JOURNAL = {Numerische Mathematik},
       VOLUME = {119},
       NUMBER = {4},
         YEAR = {2011},
          DOI = {10.1007/s00211-011-0394-z},
        PAGES = {{613--640}},
}

@article{serendipity,
       AUTHOR = {Douglas N. {A}rnold and Gerard {A}wanou},
        TITLE = {{T}he serendipity family of finite elements},
      JOURNAL = {Foundations of Computational Mathematics},
       VOLUME = {11},
       NUMBER = {3},
         YEAR = {2011},
          DOI = {10.1007/s10208-011-9087-3},
        PAGES = {{337--344}},
}

@article{sdivcurl,
       AUTHOR = {Douglas N. {A}rnold and Gerard {A}wanou},
        TITLE = {{F}inite element differential forms on cubical meshes},
      JOURNAL = {Mathematics of computation},
       VOLUME = {83},
         YEAR = {2014},
          DOI = {10.1090/S0025-5718-2013-02783-4},
        PAGES = {{1551--5170}},
}

@article{ffc,
        TITLE = {{FFC}: the {FEniCS} {Form} {Compiler}},
       AUTHOR = {Anders Logg and Kristian B. {\O}lgaard and Marie E. Rognes and Garth N. Wells},
       EDITOR = {Anders Logg and Kent-Andre Mardal and Garth N. Wells},
         YEAR = {2012},
    BOOKTITLE = {Automated Solution of Differential Equations by the
    Finite Element Method, Volume 84 of Lecture Notes in Computational
    Science and Engineering},
      CHAPTER = {11},
        PAGES = {{283--302}},
          DOI = {10.1007/978-3-642-23099-8_11},

}

@article{dolfin,
       AUTHOR = {Anders Logg and Garth N. Wells},
        TITLE = {{DOLFIN}: Automated Finite Element Computing},
      JOURNAL = {ACM Transactions on Mathematical Software},
       VOLUME = {37},
         YEAR = {2010},
          DOI = {10.1145/1731022.1731030},
}

@misc{defelement,
       AUTHOR = {{The DefElement contributors}},
        TITLE = {{D}ef{E}lement: an encyclopedia of finite element definitions},
         YEAR = {{2021}},
 HOWPUBLISHED = {\url{https://defelement.com}},
         NOTE = {[Online; accessed 26-October-2021]}
}

@article{xiao-gimbutas,
       AUTHOR = {Hong Xiao and Zydrunas Gimbutas},
        TITLE = {A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions},
      JOURNAL = {Computers & Mathematics with Applications},
       VOLUME = {59},
       NUMBER = {2},
        PAGES = {{663--676}},
         year = {2010},
          doi = {10.1016/j.camwa.2009.10.027},
}

@COMMENT{
  The authors are a list of all people with >=5 commits and >=1000 total lines of code committed to DOLFINx since 2018
  with the user with most total lines first and everyone else in alphabetical order.
}
@misc{dolfinx,
        TITLE = {DOLFINx: Next generation FEniCS problem solving environment},
        AUTHOR = {Garth N. Wells and Francesco Ballarin and Igor A. Baratta
        and Joseph P. Dean and J{\o}rgen S. Dokken and Jack S. Hale and
        Michal Habera and Chris N. Richardson and Matthew W. Scroggs and Nathan Sime},
          URL = {https://github.com/FEniCS/dolfinx},
         YEAR = {2021}
}

@COMMENT{
  The authors are a list of all people with >=5 commits and >=500 total lines of code committed to FFCx since 2018
  with the user with most total lines first and everyone else in alphabetical order.
}
@misc{ffcx,
        TITLE = {FFCx: Next generation FEniCS Form Compiler},
        AUTHOR = {Garth N. Wells and Igor A. Baratta and Michal Habera and Jack S. Hale and Chris N.
        Richardson and Matthew W. Scroggs},
          URL = {https://github.com/FEniCS/ffcx},
         YEAR = {2021}
}

@COMMENT{
  The authors are a list of all people with >=5 commits and >=1000 total lines of code committed to xtensor
  with the user with most total lines first and everyone else in alphabetical order.
}
@misc{xtensor,
        TITLE = {{xtensor}: C++ tensors with broadcasting and lazy computing},
        AUTHOR = {Johan Mabille and Thorsten Beier and David Brochart and
                  Sylvain Corlay and Tom {de Geus} and Adrien Delsalle
                  and Ullrich Koethe and {GitHub user kolibri91} and
                  Antoine Prouvost and Martin Renou and
                  {GitHub user SoundDev} and Wolf Vollprecht and Jun Zhu},
          URL = {https://github.com/xtensor-stack/xtensor},
         YEAR = {2021}
}

@article{hhj,
    AUTHOR = {{A}rnold, {D}ouglas {N}. and {W}alker, {S}hawn {W}.},
     TITLE = {{T}he {H}ellan--{H}errmann--{J}ohnson method with curved elements},
   JOURNAL = {SIAM Journal on Numberical Analysis},
    VOLUME = {58},
    NUMBER = {5},
      YEAR = {2020},
       DOI = {10.1137/19M1288723},
     PAGES = {{2829--2855}},
}

@article{symfem,
       AUTHOR = {Scroggs, Matthew W.},
        TITLE = {Symfem: a symbolic finite element definition library},
         YEAR = {2021},
      JOURNAL = {Journal of Open Source Software},
        ISSUE = {6},
       NUMBER = {64},
       VOLUME = {6},
        PAGES = {{3556}},
          DOI = {10.21105/joss.03556},
}

@TECHREPORT{ngsolve,
    author = {J. Sch\"oberl},
    title = {C++11 implementation of finite elements in {NGS}olve},
    institution = {Institute for Analysis and Scientific Computing, TU Wien},
    year = {2014},
    url = {https://www.asc.tuwien.ac.at/~schoeberl/wiki/publications/ngs-cpp11.pdf}
}

@inbook{dune,
    title = {Local Finite Elements and the dune-localfunctions Module},
    author = {Oliver Sander},
    bookTitle = {DUNE --- The Distributed and Unified Numerics Environment},
    year = {2020},
    publisher = {Springer International Publishing},
    pages = {{301--324}},
    doi = {10.1007/978-3-030-59702-3_8}
}

@article{dealii,
    author = {Bangerth, W. and Hartmann, R. and Kanschat, G.},
    title = {Deal.II---A General-Purpose Object-Oriented Finite Element Library},
    year = {2007},
    volume = {33},
    number = {4:24},
    doi = {10.1145/1268776.1268779},
    journal = {ACM Transactions on Mathematical Software},
    pages = {{1--27}},

}

@article{mfem,
    title = {MFEM: A modular finite element methods library},
    journal = {Computers & Mathematics with Applications},
    volume = {81},
    pages = {{42--74}},
    year = {2021},
    doi = {10.1016/j.camwa.2020.06.009},
    author = {Robert Anderson and Julian Andrej and Andrew Barker and Jamie Bramwell and Jean-Sylvain Camier and Jakub Cerveny and Veselin Dobrev and Yohann Dudouit and Aaron Fisher and Tzanio Kolev and Will Pazner and Mark Stowell and Vladimir Tomov and Ido Akkerman and Johann Dahm and David Medina and Stefano Zampini},
}

@unpublished{finat,
    author = {Homolya, Mikl\'os and Kirby, Robert C. and Ham, David A.},
    title = {Exposing and exploiting structure: optimal code generation for high-order finite element methods},
    year = {2017},
    ARCHIVEPREFIX = {arXiv},
    EPRINT = {1711.02473},
}

@article{bempp-cl,
       AUTHOR = {Betcke, Timo and Scroggs, Matthew W.},
        TITLE = {Bempp-cl: {A} fast {P}ython based just-in-time compiling boundary element library},
         YEAR = {2021},
      JOURNAL = {Journal of Open Source Software},
        ISSUE = {6},
       NUMBER = {59},
       VOLUME = {6},
        PAGES = {{2879}},
          DOI = {10.21105/joss.02879},
}

@article{bempp,
    title = {{Solving boundary integral problems with BEM++}},
    author = {\'{S}migaj, Wojciech and Betcke, Timo and Arridge, Simon and Phillips, Joel and Schweiger, Martin},
    year = {{2015}},
    journal = {{ACM Transactions on Mathematical Software}},
    volume = {{41}},
    number = {{2}},
    pages = {{6:1--6:40}},
    doi = {{10.1145/2590830}},
}
