Parallel characteristic finite element method for time-dependent convection-diffusion problem

Based on the overlapping-domain decomposition and parallel subspace correction method, a new parallel algorithm is established for solving time-dependent convection–diffusion problem with characteristic finite element scheme. The algorithm is fully parallel. We analyze the convergence of this algorithm, and study the dependence of the convergent rate on the spacial mesh size, time increment, iteration times and sub-domains overlapping degree. Both theoretical analysis and numerical results suggest that only one or two iterations are needed to reach to optimal accuracy at each time step. Copyright 2010 John Wiley & Sons, Ltd.