Recent progress in robust and quality Delaunay mesh generation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
SIAM Journal on Numerical Analysis
Centroidal Voronoi tessellation in universal covering space of manifold surfaces
Computer Aided Geometric Design
A Convergent Finite Volume Scheme for Diffusion on Evolving Surfaces
SIAM Journal on Numerical Analysis
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We study in this paper a finite volume approximation of linear convection-diffusion equations defined on a sphere using the spherical Voronoi meshes, in particular the spherical centroidal Voronoi meshes. The high quality of spherical centroidal Voronoi meshes is illustrated through both theoretical analysis and computational experiments. In particular, we show that the L2 error of the approximate solution is of quadratic order when the underlying mesh is given by a spherical centroidal Voronoi mesh. We also demonstrate numerically the high accuracy and the superconvergence of the approximate solutions.