Convergence and optimality of adaptive mixed finite element methods

Long Chen, Michael Holst, X. U. Jinchao

Research output: Contribution to journalArticle

56 Scopus citations

Abstract

The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure of orthogonality. a quasi-orthogonality property is proved using the fact that the error is orthogonal to the divergence free subspace, while the part of the error that is not divergence free can be bounded by the data oscillation using a discrete stability result. This discrete stability result is also used to get a localized discrete upper bound which is crucial for the proof of the optimality of the adaptive approximation.

Original languageEnglish (US)
Pages (from-to)35-53
Number of pages19
JournalMathematics of Computation
Volume78
Issue number265
DOIs
StatePublished - Jan 12 2009

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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