CONICET | Buscador de Institutos y Recursos Humanos

In this article we present an algorithm for the approximation through adaptive finite elementmethods of solutions to second order elliptic eigenvalue problems, considering Lagrange finite elementsof any degree. We show the convergence of the algorithm for simple as well as multiple eigenvalues undera minimal refinement of marked elements, for all reasonable marking strategies, and starting from anyinitial triangulation. Finally, we discuss briefly the quasi-optimality of the adaptive method and concludewith some numerical experiments that illustrate the advantages of adaptivity and the relationship betweenorder of convergence and regularity.