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...
Abstract. We prove pointwise a posteriori error estimates for semi- and fullydiscrete finite element methods for approximating the solution u to a parabolic model problem. Our esti...
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 have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the global approximation property of the Partition of Unity ...
A number of new local and parallel discretization and adaptive finite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorit...