CONICET | Buscador de Institutos y Recursos Humanos

Abstract: We consider the approximate solution with adaptive finite elements of a class of linear boundary value problems, which includes problems of `saddle point´ type. For the adaptive algorithm we suppose the following framework: refinement relies on unique quasi-regular element subdivisions and generates locally quasi-uniform grids, the finite element spaces are conforming, nested, and satisfy the inf-sup conditions, the error estimator is reliable as well as locally and discretely efficient, and marked elements are subdivided at least once. Under these assumptions, we give a sufficient and essentially necessary condition on marking for the convergence of the finite element solutions to the exact one. This condition is not only satisfied by Dörfler´s strategy, but also by the maximum strategy and the equidistribution strategy. Keywords: Adaptivity, conforming finite elements, convergence