Explicit/implicit and Crank–Nicolson domain decomposition methods for parabolic partial differential equations

Abstract

Two parallel non-overlapping domain decomposition algorithms for solving parabolic partial differential equations are proposed. The algorithms combine Crank–Nicolson scheme with implicit Galerkin finite element methods in sub-domains and explicit flux approximation along inner boundaries at each time step. Thus, parallelism can be easily achieved. L2-norm error estimates for these explicit/implicit procedures are presented, in which time step constraints are proved to be less severe than that of fully explicit schemes. Numerical experiments are also performed to verify the theoretical analysis.