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Finite volume methods on Voronoi meshes.(English)Zbl 0903.65083

Numer. Methods Partial Differ. Equations 14, No. 2, 193-212 (1998).

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)

Cited in61 Documents

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

Keywords:

finite volume methods;diffusion-convection equations;Voronoi meshes;stability;monotonicity;convergence;numerical examples

Software:

Triangle

Cite Review PDF

Full Text:DOI

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.