On the adaptive selection of the parameter in stabilized finite element approximations

Mark Ainsworth, Alejandro Ignacio Allendes Flores, Gabriel Barrenechea, Richard Andrew Robert Rankin

Research output: Contribution to journalArticle

  • 6 Citations

Abstract

A systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the Stokes problem, whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation. The approach is applied in the context of both a single fixed mesh and an adaptive mesh refinement procedure. The optimization is carried out by a derivative-free optimization algorithm and is based on minimizing a new fully computable error estimator. Numerical results are presented illustrating the theory and the performance of the estimator, together with the optimization algorithm


LanguageEnglish
Pages1585-1609
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number3
Early online date28 May 2013
DOIs
StatePublished - 2013

Fingerprint

Stabilized Finite Elements
Finite Element Approximation
Optimization Algorithm
Derivative-free Optimization
Adaptive Mesh Refinement
Stokes Problem
Error Estimator
Stabilization
Mesh
Upper bound
Minimise
Estimator
Numerical Results
Optimization
Approximation
Derivatives
Context

Keywords

  • stabililzed finite element method
  • stabilization parameter
  • computable error bounds
  • derivative-free optimization

Cite this

Ainsworth, Mark ; Allendes Flores, Alejandro Ignacio ; Barrenechea, Gabriel ; Rankin, Richard Andrew Robert. / On the adaptive selection of the parameter in stabilized finite element approximations. In: SIAM Journal on Numerical Analysis. 2013 ; Vol. 51, No. 3. pp. 1585-1609
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On the adaptive selection of the parameter in stabilized finite element approximations. / Ainsworth, Mark; Allendes Flores, Alejandro Ignacio; Barrenechea, Gabriel; Rankin, Richard Andrew Robert.

In: SIAM Journal on Numerical Analysis, Vol. 51, No. 3, 2013, p. 1585-1609.

Research output: Contribution to journalArticle

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AU - Allendes Flores,Alejandro Ignacio

AU - Barrenechea,Gabriel

AU - Rankin,Richard Andrew Robert

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N2 - A systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the Stokes problem, whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation. The approach is applied in the context of both a single fixed mesh and an adaptive mesh refinement procedure. The optimization is carried out by a derivative-free optimization algorithm and is based on minimizing a new fully computable error estimator. Numerical results are presented illustrating the theory and the performance of the estimator, together with the optimization algorithm

AB - A systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the Stokes problem, whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation. The approach is applied in the context of both a single fixed mesh and an adaptive mesh refinement procedure. The optimization is carried out by a derivative-free optimization algorithm and is based on minimizing a new fully computable error estimator. Numerical results are presented illustrating the theory and the performance of the estimator, together with the optimization algorithm

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KW - stabilization parameter

KW - computable error bounds

KW - derivative-free optimization

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JF - SIAM Journal on Numerical Analysis

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