Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

Mark Ainsworth; Richard Rankin

doi:10.1016/j.cma.2011.01.017

Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

Mark Ainsworth
, Richard Rankin^*

^*Corresponding author for this work

Research output: Journal Publication › Article › peer-review

13 Citations (Scopus)

Abstract

We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds.

Original language	English
Pages (from-to)	1909-1926
Number of pages	18
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	200
Issue number	21-22
DOIs	https://doi.org/10.1016/j.cma.2011.01.017
Publication status	Published - 1 May 2011
Externally published	Yes

Free Keywords

Computable error bounds
Elasticity
Finite element

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2011.01.017

Cite this

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title = "Realistic computable error bounds for three dimensional finite element analyses in linear elasticity",

abstract = "We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds.",

keywords = "Computable error bounds, Elasticity, Finite element",

author = "Mark Ainsworth and Richard Rankin",

note = "Funding Information: Support of the authors by the Engineering and Physical Sciences Research Council of Great Britain under the Numerical Algorithms and Intelligent Software (NAIS) for the evolving HPC platform Grant No. EP/G036136/1 is gratefully acknowledged. ",

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AU - Rankin, Richard

N1 - Funding Information: Support of the authors by the Engineering and Physical Sciences Research Council of Great Britain under the Numerical Algorithms and Intelligent Software (NAIS) for the evolving HPC platform Grant No. EP/G036136/1 is gratefully acknowledged.

PY - 2011/5/1

Y1 - 2011/5/1

N2 - We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds.

AB - We obtain a computable estimator for the energy norm of the error in piecewise affine and piecewise quadratic finite element approximations of linear elasticity in three dimensions. We show that the estimator provides guaranteed upper bounds on the energy norm of the error as well as (up to a constant and data oscillation terms) local lower bounds.

KW - Computable error bounds

KW - Elasticity

KW - Finite element

UR - https://www.scopus.com/pages/publications/79952709348

U2 - 10.1016/j.cma.2011.01.017

DO - 10.1016/j.cma.2011.01.017

M3 - Article

AN - SCOPUS:79952709348

SN - 0045-7825

VL - 200

SP - 1909

EP - 1926

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 21-22

ER -

Realistic computable error bounds for three dimensional finite element analyses in linear elasticity

Abstract

Free Keywords

ASJC Scopus subject areas

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