A radial basis Galerkin method for spherical surface Stokes equations

Abstract

Many global climate models require effcient algorithms for solv- ing the Stokes and Navier-Stokes equations with a divergence-free constraint on a spherical surface. Compactly supported radial basis functions (with centres at well distributed mesh points on a spherical surface) are more effcient than mesh based methods for computing divergence-free numerical solutions for partial differential equations on smooth surfaces. As a stepping stone towards developing an effcient radial basis algorithm for the full Navier-Stokes equations, we propose, analyse, and implement a surface divergence-free spherical radial basis Galerkin method for the Stokes equations on the unit sphere. © Austral. Mathematical Soc. 2011.