Discrete Hodge operators. Hiptmair, R. Numerische Mathematik, 90(2):265–289, 2001.
doi  abstract   bibtex   
Many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms. Discrete differential forms provide a natural and canonical approach to their discretization. However, much freedom remains concerning the choice of discrete Hodge operators, that is, discrete analogues of constitutive laws. A generic discrete Hodge operator is introduced and it turns out that most finite element and finite volume schemes emerge as its specializations. We reap the possibility of a unified convergence analysis in the framework of discrete exterior calculus.
@Article{         Hiptmair_2001aa,
  abstract      = {Many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms. Discrete differential forms provide a natural and canonical approach to their discretization. However, much freedom remains concerning the choice of discrete Hodge operators, that is, discrete analogues of constitutive laws. A generic discrete Hodge operator is introduced and it turns out that most finite element and finite volume schemes emerge as its specializations. We reap the possibility of a unified convergence analysis in the framework of discrete exterior calculus. },
  author        = {Hiptmair, Ralf},
  citable       = {1},
  doi           = {10.1007/s002110100295},
  file          = {Hiptmair_2001aa.pdf},
  group         = {casper},
  internal      = {0},
  issn          = {0945-3245},
  journal       = {Numerische Mathematik},
  keywords      = {hodge},
  langid        = {english},
  number        = {2},
  pages         = {265--289},
  title         = {Discrete {Hodge} operators},
  volume        = {90},
  year          = {2001},
  shortjournal  = {Numer. Math.}
}
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