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Finite volume methods on spheres and spherical centroidal Voronoi meshes. (English) Zbl 1099.65107

The authors develop a finite volume approximation of linear convection diffusion equations defined on a sphere using spherical Voronoi meshes. A theoretical foundation is first established by a number of theorems and lemmas and finally it is demonstrated by numerical experiments. High accuracy and superconvergence is also established.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive 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

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