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A domain splitting method for heat conduction problems in composite materials. (English) Zbl 0952.65070
The linear evolutionary heat equation is considered on a medium containing fibres placed in mutually parallel planes. These fibres are assumed dense, which approves their homogenization considered in the paper. The resulting problem then involves subdomains divided by these plates. A two-dimensional situation is then considered and discretized by (bi-)linear finite elements on triangles or quadrilaterals and the backward Euler scheme, and a noniterative overlapping domain splitting method is adapted. Convergence analysis and even rate-of-error estimates taking into account special regularity properties are presented as well as numerical experiments. The method is claimed suitable for nonlinear problems, too.

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
80A22 Stefan problems, phase changes, etc.
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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