An a Posteriori Error Estimate and Adaptive Timestep Control for a Backward Euler Discretization of a Parabolic Problem

A simple algorithm for adaptive timestep control is presented for a backward Euler discretization of a linear parabolic problem. The algorithm is based on an a posteriori error estimate involving the computed approximate solution. It is proved that, with only very rough a priori information on the exact solution, the algorithm will choose a sequence of timesteps for which the error will be controlled (up to a constant) uniformly in time on a given tolerance level.