Parallel split least-squares mixed finite element method for parabolic problem

Based on overlapping domain decomposition, a new class of parallel split least-squares (PSLS) mixed finite element methods is presented for solving parabolic problem. The algorithm is fully parallel. In the overlapping domains, the partition of unity is applied to distribute the corrections reasonably, which makes that the new method only needs one or two iteration steps to reach given accuracy at each time step while the classical Schwarz alternating methods need many iteration steps. The dependence of the convergence rate on the spacial mesh size, time increment, iteration times, and subdomains overlapping degree is analyzed. Some numerical results are reported to confirm the theoretical analysis.