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

Mark Ainsworth, R. Rankin

Research output: Contribution to journalArticle

8 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.
LanguageEnglish
Pages1114-1157
Number of pages43
JournalInternational Journal for Numerical Methods in Engineering
Volume82
Issue number9
Publication statusPublished - 28 May 2010

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Nonconforming Finite Element
Error Bounds
Elasticity
Estimator
Norm
A Posteriori Error Estimators
Finite Element Approximation
Oscillation
Higher Order
Lower bound
Upper bound
Unknown
Numerical Examples
Term
Energy

Keywords

  • finite element
  • elasticity
  • a posteriori error bounds

Cite this

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Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. / Ainsworth, Mark; Rankin, R.

In: International Journal for Numerical Methods in Engineering, Vol. 82, No. 9, 28.05.2010, p. 1114-1157.

Research output: Contribution to journalArticle

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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.

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