Analysis of the Efficiency of an a Posteriori Error Estimator for Linear Triangular Finite Elements

Abstract

This paper adresses the problem of determining upper and lower bounds for the effectivity index on the a posteriors 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. In Babuska, Plank, and Rodriguez [4] detailed numerical experimentation is given.