Parallel domain decomposition procedures of improved D–D type for parabolic problems

Two parallel domain decomposition procedures for solving initial-boundary value problems of parabolic partial differential equations are proposed. One is the extended D–D type algorithm, which extends the explicit/implicit conservative Galerkin domain decomposition procedures, given in [5], from a rectangle domain and its decomposition that consisted of a stripe of sub-rectangles into a general domain and its general decomposition with a net-like structure. An almost optimal error estimate, without the factor H − 1 / 2 given in Dawson–Dupont’s error estimate, is proved. Another is the parallel domain decomposition algorithm of improved D–D type, in which an additional term is introduced to produce an approximation of an optimal error accuracy in L 2 -norm.