Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements

M. Ainsworth, R. Rankin

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We obtain a fully computable a posteriori error bound on the broken energy norm of the error in the nonconforming finite element approximation on triangles of arbitrary order of a linear second order elliptic problem with variable permeability. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the broken energy norm of the error. This estimator is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms
LanguageEnglish
Pages3207-3232
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number6
DOIs
Publication statusPublished - 2008

Fingerprint

Nonconforming Finite Element
Triangular Element
Finite Element Approximation
Norm
Arbitrary
Energy
Estimator
Second-order Elliptic Problems
Linear Order
Permeability
Error Bounds
Triangle
Oscillation
Higher Order
Lower bound
Unknown
Term

Keywords

  • robust a posteriori error estimation
  • nonconforming finite element

Cite this

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Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. / Ainsworth, M.; Rankin, R.

In: SIAM Journal on Numerical Analysis, Vol. 46, No. 6, 2008, p. 3207-3232.

Research output: Contribution to journalArticle

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AU - Rankin, R.

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AB - We obtain a fully computable a posteriori error bound on the broken energy norm of the error in the nonconforming finite element approximation on triangles of arbitrary order of a linear second order elliptic problem with variable permeability. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the broken energy norm of the error. This estimator is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms

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