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Domain decomposition procedures for parabolic equations with discontinuous coefficients. (Chinese. English summary) Zbl 1074.65113
Summary: Explicit/implicit procedures based on domain decomposition procedures are considered for approximating solutions of parabolic equations with discontinuous coefficients. Implicit Galerkin procedures are applied in the subdomains, while conditions at the inner boundaries are calculated explicitly by a defined function from the solution at the previous time level. Thus parallelism is achieved. The procedures obey the conservative law both in the subdomains and across the inner boundaries of the subdomains. A priori error estimates and a numerical experiment are also presented.
MSC:
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35R05 PDEs with low regular coefficients and/or low regular data
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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