Superconvergence of quadratic finite elements on mildly structured grids

Yunqing Huang, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

40 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 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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