A generalized truncation method for multivalued parabolic problems

Abstract

The generalized truncation method (formerly referred to as the proximal correction method) was recently introduced for the time-discretization of parabolic variational inequalities. The main attraction of the method --- which generalizes the truncation method developed by A. Berger for obstacle problems --- is the fact that the problems to be solved at each time step are elliptic equations rather than elliptic variational inequalities.

In this paper we apply the new method to a class of problems which includes parabolic variational inequalities as a special case. The convergence results which we obtain in this general context also give rise to new results when applied to the special case of variational inequalities.

We also discuss the applications of our results to several problems that occur in various branches of applied Mathematics.