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

Research output: Contribution to journalArticle

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
Early online date28 May 2013
DOIs
StatePublished - 2013

    Research areas

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

View graph of relations