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.
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The author was partially supported by Science Foundation Ireland Grant SFI/12/IA/1683.
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Kopteva, N. Lower a posteriori error estimates on anisotropic meshes. Numer. Math. 146, 159–179 (2020). https://doi.org/10.1007/s00211-020-01137-9
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DOI: https://doi.org/10.1007/s00211-020-01137-9