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Domain decomposition method with characteristic finite element procedure for a type of parabolic systems. (Chinese. English summary) Zbl 1100.65077
Summary: A type of three-dimensional parabolic systems is studied. The domain decomposition method modified with a characteristic finite element procedure is applied. A function is defined to approximate the flux at the inner boundary by using the solution at the previous level from which we explicitly get the Neumann boundary conditions of the subproblems. Thus the subproblems are independent. An implicit Galerkin finite element procedure is applied in each subdomain. So the parallelism is achieved. A convergence analysis and an $$L^2$$ norm error estimate 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 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35K45 Initial value problems for second-order parabolic systems 65Y05 Parallel numerical computation
##### Keywords:
parallel computation; error estimate