A number of works concerning rigorous convergence theory for adaptive finite element methods (AFEM) for controlling global energy errors have appeared in recent years. However, man...
In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive proc...
We analyze an adaptive discontinuous finite element method (ADFEM) for symmetric second order linear elliptic operators. The method is formulated on nonconforming meshes made of si...
We study the convergence properties of the hp-version of the local discontinuous Galerkin finite element method for convection-diffusion problems; we consider a model problem in a ...
Paul Castillo, Bernardo Cockburn, Dominik Schö...
Abstract. Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the loca...