Posteriori Error Estimate and Automatic Time Step Control for a Backward Euler Discretization of a Parabolic Equation

摘要

A simple algorithm for automatic time step control for a backward Euler discretization of a linear parabolic problem is presented. 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 of the exact solution, the algorithm chooses the correct sequence of time steps, except possibly for a few initial steps, to guarantee global error control to a certain given tolerance.