A local defect correction technique for time-dependent problems

In this article a local defect correction technique for time-dependent problems is presented. The method is suitable for solving partial differential equations characterized by a high activity, which is mainly located, at each time, in a small part of the physical domain. The problem is solved at each time step by means of a global uniform coarse grid and a local uniform fine grid. Local and global approximation are improved iteratively. Results of numerical experiments illustrate the accuracy, the efficiency, and the robustness of the method.