Analysis of the local and parallel space-time algorithm for the heat equation

In this paper, a second-order local and parallel space-time algorithm is proposed and analyzed for the heat equation. This scheme is based on the parareal with spectral deferred correction method in time and the expandable local and parallel finite element method in space. It realizes the parallelism both in the temporal as well as in the spatial direction. We prove its stability and the optimal error estimation in L2-norm. At last, several numerical experiments are presented to demonstrate the effectiveness of our parallel scheme.