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

Mark Ainsworth, Alejandro Allendes, Gabriel R. Barrenechea, Richard Rankin

Research output: Journal PublicationArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1585-1609
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume51
Issue number3
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Computable error bounds
  • Derivative-free optimization
  • Stabilization parameter
  • Stabilized finite element method

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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