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Explicit/implicit conservative Galerkin domain decomposition procedures for parabolic problems. (English) Zbl 0746.65072

The authors consider several domain decomposition methods for the problem: u t -·(au)+bu=0 on Ω×(0,T], u n=0 on Ω×(0,T], u(x,0)=u 0 (x) on Ω, where Ω d is a bounded domain with smooth boundary and n is the outward normal.

The procedures use explicit calculations on the boundaries of the subdomains to predict the flux. They are also conservative in the sense that the surfaces of the subdomains do not serve as sources or sinks.

Error estimates are given in terms of solutions of some related elliptic problems.

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