Adaptive Finite Element Methods for Parabolic Problems

We continue our work on adaptive nite element methods with a study of time discretization of analytic semigroups. We prove optimal a priori and a posteriori error estimates for the discontinuous Galerkin method showing, in particular, that analytic semigroups allow long-time integration without error accumulation. 1. Introduction This paper is a continuation of the series of papers 1], 2], 3], 4], 5] on adap-tive nite element methods for parabolic problems. The method considered is the discontinuous Galerkin method (the dG-method) based on a space-time nite element discretization with piecewise polynomial basis functions that are continuous in space and discontinuous in time. In 1], 2], 3], 4], 5] we proved optimal a priori and a posteriori error estimates for the dG-method for parabolic problems,