Generalized Gaffney inequality and discrete compactness for discrete differential forms

Juncai He, Kaibo Hu, Jinchao Xu

Research output: Contribution to journalArticle

Abstract

We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on s-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have been established for edge elements with weakly imposed divergence-free conditions and used in the analysis of nonlinear and eigenvalue problems. In this paper, we generalize these results to discrete differential forms, not necessarily with strongly or weakly imposed constraints. The analysis relies on a new Hodge mapping and its approximation property. As an application, we show Lp estimates for several finite element approximations of the scalar and vector Laplacian problems.

Original languageEnglish (US)
Pages (from-to)781-795
Number of pages15
JournalNumerische Mathematik
Volume143
Issue number4
DOIs
StatePublished - Dec 1 2019

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Electromagnetism
Differential Forms
Compactness
Edge Elements
Lp Estimates
Lipschitz Domains
Divergence-free
Approximation Property
Finite Element Approximation
Eigenvalue Problem
Nonlinear Problem
Scalar
Finite Element
Generalise

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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Generalized Gaffney inequality and discrete compactness for discrete differential forms. / He, Juncai; Hu, Kaibo; Xu, Jinchao.

In: Numerische Mathematik, Vol. 143, No. 4, 01.12.2019, p. 781-795.

Research output: Contribution to journalArticle

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