Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity

Mark Ainsworth; R. Rankin

Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity

Mark Ainsworth, R. Rankin

Mathematics And Statistics

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

10 Citations (Scopus)

Abstract

We obtain fully computable a posteriori error estimators for the energy norm of the error in second-order conforming and nonconforming finite element approximations in planar elasticity. These estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error. The estimators are shown to also provide local lower bounds, up to a constant and higher-order data oscillation terms. Numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator.

Original language	English
Pages (from-to)	1114-1157
Number of pages	43
Journal	International Journal for Numerical Methods in Engineering
Volume	82
Issue number	9
Publication status	Published - 28 May 2010

Keywords

finite element
elasticity
a posteriori error bounds

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ADAPTIVE NUMERICAL METHODS FOR OPTOELECTRONIC DEVICES PFACT 69
Ainsworth, M., Mottram, N. & Ramage, A.
EPSRC (Engineering and Physical Sciences Research Council)
2/04/07 → 30/11/10
Project: Research

Cite this

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title = "Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity",

abstract = "We obtain fully computable a posteriori error estimators for the energy norm of the error in second-order conforming and nonconforming finite element approximations in planar elasticity. These estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error. The estimators are shown to also provide local lower bounds, up to a constant and higher-order data oscillation terms. Numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator.",

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AU - Ainsworth, Mark

AU - Rankin, R.

PY - 2010/5/28

Y1 - 2010/5/28

N2 - We obtain fully computable a posteriori error estimators for the energy norm of the error in second-order conforming and nonconforming finite element approximations in planar elasticity. These estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error. The estimators are shown to also provide local lower bounds, up to a constant and higher-order data oscillation terms. Numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator.

AB - We obtain fully computable a posteriori error estimators for the energy norm of the error in second-order conforming and nonconforming finite element approximations in planar elasticity. These estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error. The estimators are shown to also provide local lower bounds, up to a constant and higher-order data oscillation terms. Numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator.

KW - finite element

KW - elasticity

KW - a posteriori error bounds

UR - http://onlinelibrary.wiley.com/doi/10.1002/nme.2799/abstract

UR - http://dx.doi.org/10.1002/nme.2799

M3 - Article

VL - 82

SP - 1114

EP - 1157

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 9

ER -

Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity

Abstract

Keywords

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ADAPTIVE NUMERICAL METHODS FOR OPTOELECTRONIC DEVICES PFACT 69

Cite this