Basic Problems of A-Posteriori Error Estimation

摘要

This paper addresses basic questions regarding reliability of a-posteriori errorestimation. It analyzes in detail an a-posteriori estimator for linear elements on triangular meshes. It gives the bounds of the effectivity index depending on the geometry of the triangles and smoothness of the approximated solution. The theoretical results are in concordance with the results of our numerical experiments. The second part analyzes in one dimensional setting a one parametric family of the estimators and their optimal selection for adaptively constructed meshes.