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

Mitsuhiro T. Nakao; Nobito Yamamoto; Yoshitaka Watanabe

doi:10.1016/S0377-0427(98)00035-1

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

Mitsuhiro T. Nakao^*, Nobito Yamamoto, Yoshitaka Watanabe

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 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 language	English
Pages (from-to)	137-158
Number of pages	22
Journal	Journal of Computational and Applied Mathematics
Volume	91
Issue number	1
DOIs	https://doi.org/10.1016/S0377-0427(98)00035-1
Publication status	Published - 1998 Apr 24
Externally published	Yes

Keywords

Computable error
Guaranteed error bounds
Stokes equations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0377-0427(98)00035-1

Cite this

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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.",

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AU - Yamamoto, Nobito

AU - Watanabe, Yoshitaka

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Y1 - 1998/4/24

N2 - 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.

AB - 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.

KW - Computable error

KW - Guaranteed error bounds

KW - Stokes equations

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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