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

@article{cbcaf04bc2944433ae172aadd5fdc2fb,

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.",

keywords = "computable error bounds, finite element approximation, nonpolygonal domains.",

author = "Mark Ainsworth and Richard Rankin",

note = "Publisher Copyright: {\textcopyright} The authors 2016.",

year = "2017",

month = apr,

day = "1",

doi = "10.1093/imanum/drw040",

language = "English",

volume = "37",

pages = "604--645",

journal = "IMA Journal of Numerical Analysis",

issn = "0272-4979",

publisher = "Oxford University Press",

number = "2",

}

TY - JOUR

T1 - Computable error bounds for finite element approximation on nonpolygonal domains

AU - Ainsworth, Mark

AU - Rankin, Richard

N1 - Publisher Copyright: © The authors 2016.

PY - 2017/4/1

Y1 - 2017/4/1

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 - http://www.scopus.com/inward/record.url?scp=85019107516&partnerID=8YFLogxK

U2 - 10.1093/imanum/drw040

DO - 10.1093/imanum/drw040

M3 - Article

AN - SCOPUS:85019107516

SN - 0272-4979

VL - 37

SP - 604

EP - 645

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

Access to Document

Other files and links

Fingerprint

Cite this