Optimal anisotropic meshes for minimizing interpolation errors in L p-norm

Long Chen, Pengtao Sun, Jinchao Xu

Research output: Contribution to journalArticle

103 Scopus citations

Abstract

In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and obtain optimal monitor functions from the viewpoint of minimizing interpolation error in the Lp norm. Some numerical examples are also given to support the theoretical estimates.

Original languageEnglish (US)
Pages (from-to)179-204
Number of pages26
JournalMathematics of Computation
Volume76
Issue number257
DOIs
StatePublished - Jan 1 2007

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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