Un estimador de error residual para el método de los elementos finitos

Abstract

Residual-type error estimators are based on solving the error equation. This paper presents an error estimator which solves local error problems using elementary submeshes. Each elementary problem is solved using trivial Dirichlet boundary conditions. Thus, a first estimate is obtained. This estimate accounts only for the error in the interior of the elements and, consequently, the effect of the flux jump accross the element edges is not included. In a second phase the flux jumps are accounted for. However, in contrast with other residual-type error estimators, this is done without computing the jumps. This precludes the need of balancing the jumps along the edges and obtains the error fluxes. This second phase follows the same approach of the first one: local problems are solved using submeshes. The subdomains associated with this second set of local problems overlap the elements and cover their edges. The estimate associated with this second phase is constrained to additional restrictions allowing to sum up the contributions of the two phases. The complete estimate computed from the combination of the two phases gives excellent results in the application examples compared to existing error estimators.

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