Fully computable robust a posteriori error bounds for singularly perturbed reaction–diffusion problems

Mark Ainsworth, Tomas Vejchodsky

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14 Citations (Scopus)
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Abstract

A procedure for the construction of robust, upper bounds for the error in
the finite element approximation of singularly perturbed reaction–diffusion problems was presented in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem exactly and this fact was recognised in the above work where it was indicated that the limitation would be addressed in a subsequent article. We view the present work as fulfilling that promise and as completing the investigation begun in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999) by removing the obligation to solve a local problem exactly. The resulting new estimator is indeed fully computable and the first to provide fully computable, robust upper bounds in the setting of singularly perturbed problems discretised by the finite element method
Original languageEnglish
Pages (from-to)219-243
Number of pages25
JournalNumerische Mathematik
Volume119
Issue number2
Early online date24 Jun 2011
DOIs
Publication statusPublished - 2011

Keywords

  • reaction–diffusion problems
  • finite elementmethod

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