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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