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Parallel Galerkin domain decomposition procedures for parabolic equation on general domain. (English) Zbl 1173.65061
The authors put forward parallel Galerkin domain decomposition methods for parabolic partial differential equations with homogeneous Neumann conditions on domains of dimension between one and three. Implicit Galerkin methods are used on the subdomains, and either an explicit flux calculation on the interdomain boundaries by an integral mean method or extrapolation serve to predict the inner-boundary conditions. L 2 -norm error bounds are proven for both procedures, which improve earlier results. The procedures are conservative both in the subdomains and across interboundaries. The explicit nature of the flux prediction induces a step-size restriction necessary to preserve stability. Numerical experiments illustrate the theoretical results.

MSC:
65M55Multigrid methods; domain decomposition (IVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
35K15Second order parabolic equations, initial value problems
65Y05Parallel computation (numerical methods)
65M12Stability and convergence of numerical methods (IVP of PDE)