Du, Qiang; Ju, Lili Finite volume methods on spheres and spherical centroidal Voronoi meshes. (English) Zbl 1099.65107 SIAM J. Numer. Anal. 43, No. 4, 1673-1692 (2005). 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. Reviewer: Prabhat Kumar Mahanti (Saint John) Cited in 11 Documents 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 Keywords:error estimates; numerical experiments; superconvergence Software:STRIPACK PDFBibTeX XMLCite \textit{Q. Du} and \textit{L. Ju}, SIAM J. Numer. Anal. 43, No. 4, 1673--1692 (2005; Zbl 1099.65107) Full Text: DOI