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Corrected explicit-implicit domain decomposition algorithms for two-dimensional semilinear parabolic equations. (English) Zbl 1183.65120

This paper is concerned with a corrected explicit-implicit domain decomposition algorithm for the numerical approximation of semilinear parabolic problems on distributed memory processors. First, the spatial domain is divided into smaller parallel strips and cells by straightlines interfaces. At each time level, predictive values are obtained by using the forward Euler scheme on the man-made interior boundary and then subdomain solutions are obtained by means of the backward Euler scheme. Once the subdomain solutions are available, the interface solutions are recomputed by the fully implicit scheme. By using the Leray-Schauder fixed point theorem combined with the discrete energy method, the authors prove that the algorithm is uniquely solvable, unconditionally stable and convergent. In particular, an improved error estimate is achieved. Various numerical results are presented to confirm the stability and accuracy of the method.

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
35K58 Semilinear parabolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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