A Novel Galerkin Method for Solving PDEs on the Sphere Using Highly Localized Kernel Bases

摘要

We present a novel Galerkin method for solving partial differential equationson the sphere. The problem is discretized by a highly localized basis which iseasily constructed. The stiffness matrix entries are computed by a recentlydeveloped quadrature formula unique to the localized bases we consider. Wepresent error estimates and investigate the stability of the discrete stiffnessmatrix. Implementation and numerical experiments are discussed.