Convergence of a time discrete Galerkin method for semilinear parabolic equations

Abstract. We approximate the solution of initial boundary value problems of semilinear parabolic equations by time-discrete discontinuous finite element methods. We propose an approach leading to optimal order-regularity a priori error bounds. Our approach is based on techniques developed for the numerical approximation in bifurcation theory for mildly nonlinear elliptic equations and on the stability analysis of the method for linear parabolic problems with mesh dependent norms. 10 − 12 − 2002 1