Convergence of adaptive finite element methods for eigenvalue problems

Abstract

In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.


Published: Mathematical Models and Methods in Applied Sciences (M3AS), Vol. 19, No. 5 (2009), 721--747.