Asymptotically exact a posteriori error estimators, Part I: Grids with superconvergence

Randolph E. Bank, X. U. Jinchao

Research output: Contribution to journalArticle

116 Citations (Scopus)

Abstract

In Part I of this work, we develop superconvergence estimates for piecewise linear finite element approximations on quasi-uniform triangular meshes where most pairs of triangles sharing a common edge form approximate parallelograms. In particular, we first show a superconvergence of the gradient of the finite element solution u h and to the gradient of the interpolant u I, We then analyze a postprocessing gradient recovery scheme, showing that Q h∇u h is superconvergent approximation to ∇u. Here Q h is the global L 2 projection. In Part II, we analyze a superconvergent gradient recovery scheme for general unstructured, shape regular triangulations. This is the foundation for an a posteriori error estimate and local error indicators.

Original languageEnglish (US)
Pages (from-to)2294-2312
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume41
Issue number6
DOIs
StatePublished - Dec 1 2003

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Gradient Recovery
A Posteriori Error Estimators
Superconvergence
Gradient
Grid
Recovery
Error Indicator
Parallelogram
Triangular Mesh
A Posteriori Error Estimates
Finite Element Solution
Linear Approximation
Interpolants
Triangulation
Finite Element Approximation
Post-processing
Piecewise Linear
Triangle
Sharing
Projection

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Asymptotically exact a posteriori error estimators, Part I : Grids with superconvergence. / Bank, Randolph E.; Jinchao, X. U.

In: SIAM Journal on Numerical Analysis, Vol. 41, No. 6, 01.12.2003, p. 2294-2312.

Research output: Contribution to journalArticle

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