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Finite volume methods on Voronoi meshes. (English) Zbl 0903.65083
The article is concerned with finite volume methods for (stationary) diffusion-convection equations on convex domains, with Dirichlet boundary conditions. The author proposes two schemes on Voronoi meshes and investigates their stability, monotonicity, and convergence properties. Several numerical examples, partly diffusion and partly convection dominated, illustrate the theoretical convergence results.
Reviewer: M.Plum (Karlsruhe)

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
Software:
Triangle
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