Posteriori error estimates for the Stokes problem

Randolph E. Bank, Bruno D. Welfert

Research output: Contribution to journalArticle

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Abstract

An a posteriori error estimate is derived and analyzed for the mini-element discretization of the Stokes equations. The estimate is based on the solution of a local Stokes problem in each element of the finite element mesh, using spaces of quadratic bump functions for both velocity and pressure errors. This results in solving a 9 × 9 system which reduces to two easily invertible 3 × 3 systems. Comparisons with other estimates based on a Petrov-Galerkin solution are used in this analysis, which shows that it provides a reasonable approximation of the actual discretization error. Numerical experiments clearly show the efficiency of such an estimate in the solution of self-adaptive mesh refinement procedures.

Original languageEnglish (US)
Pages (from-to)591-623
Number of pages33
JournalSIAM Journal on Numerical Analysis
Volume28
Issue number3
DOIs
StatePublished - Jan 1 1991

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ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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