Pollution Error in the h-Version of the Finite Element Method and the LocalQuality of A-Posteriori Error Estimators

摘要

In this work we study the pollution-error in the h-version of the finite elementmethod and its effect on the local quality of a-posteriori error estimators. We show that the pollution-effect in an interior subdomain depends on the relationship between the mesh inside and outside the subdomain and the smoothness of the exact solution. We also demonstrate that it is possible to guarantee the quality of local error-estimators in the interior of a finite-element mesh-patch of interest by employing meshes which are sufficiently refined outside the patch.