Numerische Mathematik

, Volume 90, Issue 2, pp 265–289

Discrete Hodge operators

  • R. Hiptmair
Original article

DOI: 10.1007/s002110100295

Cite this article as:
Hiptmair, R. Numer. Math. (2001) 90: 265. doi:10.1007/s002110100295


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.

Mathematics Subject Classification (1991): 39A05, 58A10, 65N06, 65P05, 65N15 

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • R. Hiptmair
    • 1
  1. 1.Universität Tübingen, Sonderforschungsbereich 382, Auf der Morgenstelle 10, 72076 Tübingen, Germany; e-mail: ralf@hiptmair.deDE

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