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Zbl 1173.65061
Ma, Keying; Sun, Tongjun; Yang, Danping
Parallel Galerkin domain decomposition procedures for parabolic equation on general domain. (English)
[J] Numer. Methods Partial Differ. Equations 25, No. 5, 1167-1194 (2009). ISSN 0749-159X; ISSN 1098-2426/e

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.
[Othmar Koch (Baden)]

MSC 2000:: *65M55 Multigrid methods; domain decomposition (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
65M15 Error bounds (IVP of PDE)
35K15 Second order parabolic equations, initial value problems
65Y05 Parallel computation (numerical methods)
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: domain decomposition method; implicit Galerkin method; error bounds; parallel computation; extrapolation method; integral mean method; parabolic equation; stability; numerical experiments

Cited in: Zbl 1225.65096 Zbl 1222.65106

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