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Lower a posteriori error bounds obtained using the standard bubble functionapproach are reviewed in the context of anisotropic meshes. A numerical exampleis given that clearly demonstrates that the short-edge jump residual terms insuch bounds are not sharp. Hence, for linear finite element approximations ofthe Laplace equation in polygonal domains, a new approach is employed to obtainessentially sharper lower a posteriori error bounds and thus to show that theupper error estimator in the recent paper [N. Kopteva, Numer. Math., 137(2017), 607-642] is efficient on certain anisotropic meshes.

Lower a posteriori error estimates on anisotropic meshes