Summary.
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.
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Received November 26, 1999 / Revised version received November 2, 2000 / Published online May 30, 2001
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Hiptmair, R. Discrete Hodge operators. Numer. Math. 90, 265–289 (2001). https://doi.org/10.1007/s002110100295
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DOI: https://doi.org/10.1007/s002110100295