Articulo
On the asymptotic exactness of error estimators for linear triangular finite elements
Registro en:
issn:0029-599x
issn:0945-3245
Autor
Durán, Ricardo Guillermo
Muschietti, María Amelia
Rodríguez, Rodolfo
Institución
Resumen
This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of elliptic problems. We analyze two estimators based on recovery operators for the gradient of the approximate solution. By using superconvergence results we prove their asymptotic exactness under regularity assumptions on the mesh and the solution. One of the estimators can be easily computed in terms of the jumps of the gradient of the finite element approximation. This estimator is equivalent to the error in the energy norm under rather general conditions. However, we show that for the asymptotic exactness, the regularity assumption on the mesh is not merely technical. While doing this, we analyze the relation between superconvergence and asymptotic exactness for some particular examples. Facultad de Ciencias Exactas