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Solving diffusion equations with rough coefficients in rough grids. (English) Zbl 0874.65062

The main goal of the paper is the description and investigation a new finite difference algorithm for solving diffusion equations with rough coefficients in strongly heterogeneous and nonisotropic media on general locally rectangular grids. The algorithm is derived using the method of support operators, which requires that the diffusion equation can be written in terms of invariant operators, in case of divergence and gradient. The performance of the suggested algorithm is compared with some other algorithms for problems with smooth coefficients and regular grids.
The paper gives the first application of this method to the solution of diffusion problems in heterogeneous and nonisotropic media. For rectangular grids the discrete operators reduce to well-known discrete operators, and the treatment of discontinuous conductivity coefficients in the case of isotropic media is equivalent to the well-known harmonic-averaging procedure. Comparison with standard schemes and examples of numerical validation are presented.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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