Convergence and quasi-optimality of an adaptive finite element method for controlling L2 errors

In this paper, a contraction property is proved for an adaptive finite element method for controlling the global L 2 error on convex polyhedral domains. Furthermore, it is shown that the method converges in L 2 with the best possible rate. The method that is analyzed is the standard adaptive method except that, if necessary, additional refinements are made to keep the meshes sufficiently mildly graded. This modification does not compromise the quasi-optimality of the resulting algorithm