An adaptive multilevel approach to parabolic equations. II. Variable-order time discretization based on a multiplicative error correction

In continuation of part I this paper develops a variable-order time discretization in Hilbert space based on a multiplicative error correction. Matching of time and space errors as explained in part I allows to construct an adaptive multilevel discretization of the parabolic problem. In contrast to the extrapolation method in time, which has been used in part I, the new time discretization allows us to separate space and time errors and further to solve fewer elliptic subproblems with less effort-a feature which is essential in view of the application to space dimensions greater than one. Numerical examples for space dimension one are included which clearly indicate the improvement.