A radial basis Galerkin method for spherical surface Stokes equations

Abstract

Many global climate models require efficient algorithms for solving 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 efficient than mesh based methods for computing divergence-free numerical solutions for partial differential equations on smooth surfaces. As a stepping stone towards developing an efficient 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. References

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