Posteriori error estimates for the Stokes problem

Randolph E. Bank, Bruno Welfert

Research output: Contribution to journalArticle

81 Citations (Scopus)

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
StatePublished - Jun 1991
Externally publishedYes

Fingerprint

Stokes Problem
Error Estimates
Estimate
Petrov-Galerkin
Adaptive Mesh Refinement
Discretization Error
A Posteriori Error Estimates
Stokes Equations
Invertible
Discretization
Numerical Experiment
Mesh
Finite Element
Approximation
Experiments

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Posteriori error estimates for the Stokes problem. / Bank, Randolph E.; Welfert, Bruno.

In: SIAM Journal on Numerical Analysis, Vol. 28, No. 3, 06.1991, p. 591-623.

Research output: Contribution to journalArticle

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