ABSTRACT
Abstract . We survey the development of finite element methods for parabolic equa tions . We start to discuss the analysis of Douglas and Dupont ( 1 970) and the intro duction of the Ritz projection by Wheeler ( 1973) with its consequences for optimal order L2-convergence and superconvergence. We proceed to discuss Loo-estimates, in particular maximum norm stability results of Schatz, Thomee, and Wahlbin ( 1 980) in two space dimensions, Crouzeix, Thomee, and Wahlbin ( 1 980) in one space dimension, and Fujii ( 1973) for the lumped mass method in two dimensions . In a final part we discuss variable time steps and the use of the discontinuous Galerkin method accord ing to Eriksson, Johnson, and Thomee ( 1 985) , and touch upon the a posteriori error estimates of Eriksson and Johnson ( 1 987) with application to adaptive time stepping.
