Lower a posteriori error estimates on anisotropic meshes

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Abstract

Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such bounds are not sharp. Hence, for linear finite element approximations of the Laplace equation in polygonal domains, a new approach is employed to obtain essentially sharper lower a posteriori error bounds and thus to show that the upper error estimator in the recent paper (Kopteva in Numer Math 137:607–642, 2017) is efficient on partially structured anisotropic meshes.

Original languageEnglish
Pages (from-to)159-179
Number of pages21
JournalNumerische Mathematik
Volume146
Issue number1
DOIs
Publication statusPublished - 1 Sep 2020

Keywords

  • Anisotropic triangulation
  • Estimator efficiency
  • Lower a posteriori error estimate

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