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

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

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10 Citations (Scopus)
60 Downloads (Pure)


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
Issue number3
Early online date28 May 2013
Publication statusPublished - 2013


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


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