Parallel domain decomposition procedures of improved D-D type for parabolic problems |
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Authors: | Danping Yang |
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Affiliation: | Department of Mathematics, East China Normal University, Shanghai, 200241, PR China |
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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 L2-norm. |
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Keywords: | 65N12 65N15 65N30 65N55 |
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