Superconvergence of quadratic finite elements on mildly structured grids

Yunqing Huang, Jinchao Xu

Research output: Contribution to journalArticle

38 Scopus citations

Abstract

Superconvergence estimates are studied in this paper on quadratic finite element discretizations for second order elliptic boundary value problems on mildly structured triangular meshes. For a large class of practically useful grids, the finite element solution uh is proven to be superclose to the inter-polant uI and as a result a postprocessing gradient recovery scheme for uh can be devised. The analysis is based on a number of carefully derived identities. In addition to its own theoretical interests, the result in this paper can be used for deriving asymptotically exact a posteriori error estimators for quadratic finite element methods.

Original languageEnglish (US)
Pages (from-to)1253-1268
Number of pages16
JournalMathematics of Computation
Volume77
Issue number263
DOIs
StatePublished - Jul 1 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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