Robust a posteriori error estimation for non-conforming finite element approximation

M. Ainsworth

Research output: Contribution to journalArticle

80 Citations (Scopus)

Abstract

The equilibrated residual method for a posteriori error estimation is extended to nonconforming finite element schemes for the approximation of linear second order elliptic equations where the permeability coefficient is allowed to undergo large jumps in value across interfaces between differing media. The estimator is shown to provide a computable upper bound on the error and, up to a constant depending only on the geometry, provides two-sided bounds on the error. The robustness of the estimator is also studied and the dependence of the constant on the jumps in permeability is given explicitly.
Original languageEnglish
Pages (from-to)2320-2341
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume42
Issue number6
DOIs
Publication statusPublished - 2005

Fingerprint

Nonconforming Finite Element
A Posteriori Error Estimation
Finite Element Approximation
Permeability
Error analysis
Jump
Estimator
Second Order Elliptic Equations
Hydraulic conductivity
Linear Order
Upper bound
Robustness
Geometry
Coefficient
Approximation

Keywords

  • robust a posteriori error estimation
  • nonconforming finite element
  • Crouzeix--Raviart element
  • saturation assumption

Cite this

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Robust a posteriori error estimation for non-conforming finite element approximation. / Ainsworth, M.

In: SIAM Journal on Numerical Analysis, Vol. 42, No. 6, 2005, p. 2320-2341.

Research output: Contribution to journalArticle

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KW - robust a posteriori error estimation

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KW - Crouzeix--Raviart element

KW - saturation assumption

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