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A finite volume method for the approximation of diffusion operators on distorted meshes. (English) Zbl 0949.65101
This paper deals with diffusion equations on planar domains with arbitrarily irregular grids. The author proposes a finite volume method on the given grid, and it is coupled to another finite volume method on a dual grid. It is shown that the resulting matrix is positive definite, even though it may not be diagonally dominant. Several computational examples are given.

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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