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.} }

Downloads: 0