Interior maximum norm estimates for finite element discretizations of the Stokes equations

R. Narasimhan, I. Babuška

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Interior estimates are proved in the L norm for stable finite element discretizations of the Stokes equations on translation invariant meshes. These estimates yield information about the quality of the finite element solution in subdomains a positive distance from the boundary. While they have been established for second-order elliptic problems, these interior, or local, maximum norm estimates for the Stokes equations are new. By applying finite differenciation methods on a translation invariant mesh, we obtain optimal convergence rates in the mesh size h in the maximum norm. These results can be used for analyzing superconvergence in finite element methods for the Stokes equations.

Original languageEnglish
Pages (from-to)251-260
Number of pages10
JournalInternational Journal of Phytoremediation
Volume86
Issue number2
DOIs
StatePublished - Feb 2007

Keywords

  • 2000 Mathematics Subject Classifications: Primary: 65N15
  • Interior error estimates
  • Mixed finite element method
  • Secondary: 65N30
  • Stokes equations

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