Analysis of the Efficiency of an A-Posteriori Error Estimator for LinearTriangular Finite Elements

摘要

This paper addresses the problem of determining upper and lower bounds for theeffectivity index on the a-posteriori estimate of the error in the finite element method. These bounds are given explicitly for a certain concrete estimator for linear elements and unstructured triangular meshes. They depend strongly on the geometry of the triangles and (relatively weakly) on the smoothness of the solution. An example shows that the bounds are not over pessimistic.