A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations

Mitsuhiro T. Nakao, Nobito Yamamoto, Yoshitaka Watanabe

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We describe a method to estimate the guaranteed error hounds of the finite element solutions for the Stokes problem in mathematically rigorous sense. We show that an a posteriori error can be computed by using the numerical estimates of a constant related to the so-called inf-sup condition for the continuous problem. Also a method to derive the constructive a priori error bounds are considered. Some numerical examples which confirm us the expected rate of convergence are presented.

Original languageEnglish
Pages (from-to)137-158
Number of pages22
JournalJournal of Computational and Applied Mathematics
Volume91
Issue number1
DOIs
Publication statusPublished - 1998 Apr 24
Externally publishedYes

Fingerprint

A Priori Error Bounds
Stokes Equations
Finite Element Solution
Inf-sup Condition
Stokes Problem
Estimate
Rate of Convergence
Numerical Examples

Keywords

  • Computable error
  • Guaranteed error bounds
  • Stokes equations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations. / Nakao, Mitsuhiro T.; Yamamoto, Nobito; Watanabe, Yoshitaka.

In: Journal of Computational and Applied Mathematics, Vol. 91, No. 1, 24.04.1998, p. 137-158.

Research output: Contribution to journalArticle

Nakao, Mitsuhiro T. ; Yamamoto, Nobito ; Watanabe, Yoshitaka. / A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations. In: Journal of Computational and Applied Mathematics. 1998 ; Vol. 91, No. 1. pp. 137-158.
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