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

Authors:
Danping Yang
Affiliations:
Department of Mathematics, East China Normal University, Shanghai, 200241, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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.