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

Mark Ainsworth; Richard Andrew Robert 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 Andrew Robert Rankin

Mathematics And Statistics

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13 Citations (Scopus)

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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 - May 2011

Keywords

finite element
elasticity
computable error bounds

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10.1016/j.cma.2011.01.017

8marr3delasticitySubmitted manuscript, 394 KB

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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. ",

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author = "Mark Ainsworth and Rankin, \{Richard Andrew Robert\}",

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doi = "10.1016/j.cma.2011.01.017",

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AU - Ainsworth, Mark

AU - Rankin, Richard Andrew Robert

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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 - finite element

KW - elasticity

KW - computable error bounds

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

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

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