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A non-overlapping domain decomposition method for the advection-diffusion problem. (English) Zbl 0959.65139
The authors consider the application of a non-overlapping domain decomposition method to the solution of advection-diffusion problems. The method under consideration is an iteration-by-subdomains algorithm with transmission conditions of Robin type using streamline-diffusion finite element discretization. A posteriori error estimates bounding the error on subdomains by the interface error of the subdomain solution are obtained. These estimates help to construct appropriate interface conditions which are confirmed by numerical examples.

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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