A-POSTERIORI ERROR ESTIMATION FOR STANDARD FINITE-ELEMENT ANALYSIS

A new residual type estimator based on projections of the error on sub spaces of locally-supported functions is presented. The estimator is d efined by a standard element-by-element refinement. First, an approxim ation of the energy norm of the error is obtained solving local proble ms with homogeneous Dirichlet boundary conditions. A later enrichment of the estimation is performed by adding the contributions of projecti ons on a new family of subspaces. This estimate is a lower bound of th e measure of the actual error. The estimator does not need to approxim ate local boundary conditions for the error equation. Therefore, compu tation of flux jumps is not necessary. Moreover, the estimator can be applied in mixed meshes containing elements of different shapes and it s implementation in a standard finite element code is straightforward. The presented results show the effectiveness of the estimator approxi mating both the distribution and the global measure of the error, as w ell as its usefulness in adaptive procedures. (C) 1998 Elsevier Scienc e S.A. All rights reserved.