Computable error bounds for finite element approximation on nonpolygonal domains

Mark Ainsworth; Richard Rankin

doi:10.1093/imanum/drw040

Computable error bounds for finite element approximation on nonpolygonal domains

Mark Ainsworth, Richard Rankin

Research output: Journal Publication › Article › peer-review

2 Citations (Scopus)

Abstract

We consider the case of piecewise affine approximation of the solution to the Poisson problem, with pure Neumann boundary data, on nonpolygonal domains. A computable, guaranteed upper bound on the energy norm of the error in such a finite element approximation is obtained. The estimator takes the effect of the boundary approximation into account and provides, up to a constant and oscillation terms, local lower bounds on the energy norm of the error.

Original language	English
Pages (from-to)	604-645
Number of pages	42
Journal	IMA Journal of Numerical Analysis
Volume	37
Issue number	2
DOIs	https://doi.org/10.1093/imanum/drw040
Publication status	Published - 1 Apr 2017
Externally published	Yes

Keywords

computable error bounds
finite element approximation
nonpolygonal domains.

ASJC Scopus subject areas

General Mathematics
Computational Mathematics
Applied Mathematics

Access to Document

10.1093/imanum/drw040

Cite this

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title = "Computable error bounds for finite element approximation on nonpolygonal domains",

abstract = "We consider the case of piecewise affine approximation of the solution to the Poisson problem, with pure Neumann boundary data, on nonpolygonal domains. A computable, guaranteed upper bound on the energy norm of the error in such a finite element approximation is obtained. The estimator takes the effect of the boundary approximation into account and provides, up to a constant and oscillation terms, local lower bounds on the energy norm of the error.",

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author = "Mark Ainsworth and Richard Rankin",

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AU - Rankin, Richard

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N2 - We consider the case of piecewise affine approximation of the solution to the Poisson problem, with pure Neumann boundary data, on nonpolygonal domains. A computable, guaranteed upper bound on the energy norm of the error in such a finite element approximation is obtained. The estimator takes the effect of the boundary approximation into account and provides, up to a constant and oscillation terms, local lower bounds on the energy norm of the error.

AB - We consider the case of piecewise affine approximation of the solution to the Poisson problem, with pure Neumann boundary data, on nonpolygonal domains. A computable, guaranteed upper bound on the energy norm of the error in such a finite element approximation is obtained. The estimator takes the effect of the boundary approximation into account and provides, up to a constant and oscillation terms, local lower bounds on the energy norm of the error.

KW - computable error bounds

KW - finite element approximation

KW - nonpolygonal domains.

UR - https://www.scopus.com/pages/publications/85019107516

U2 - 10.1093/imanum/drw040

DO - 10.1093/imanum/drw040

M3 - Article

AN - SCOPUS:85019107516

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JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 2

ER -

Computable error bounds for finite element approximation on nonpolygonal domains

Abstract

Keywords

ASJC Scopus subject areas

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