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A domain decomposition discretization of parabolic problems. (English) Zbl 1130.65097

A domain decomposition method is presented for parabolic problems based on the discretization of the problem which leads to a domain decomposition algorithm as a direct method. The stability and convergence of this algorithm are analyzed. The authors obtain an optimal bound for the error. Numerical experiments are carried out to illustrate the theoretical results.

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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References:

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