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A mixed finite volume scheme for anisotropic diffusion problems on any grid. (English) Zbl 1109.65099

A new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which is easy to implement is presented here [cf. R. A. Klausen and T. F. Russell [Comput. Geosci, 8, No. 4, 341–377 (2004)]. This can apply to any type of grid in any space dimension, with very few conditions on the control volumes. Accurate results are obtained on fairly irregular grids in the case of highly heterogeneous anisotropic problems. Efficiency of the scheme is also shown on several types of grids.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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