A Novel Galerkin Method for Solving PDEs on the Sphere Using Highly Localized Kernel Bases
This work offers a new discretization approach for PDEs on the sphere, potentially benefiting computational geophysics and climate modeling, but the results are preliminary without concrete performance numbers.
The paper introduces a Galerkin method for solving PDEs on the sphere using highly localized kernel bases, with a specialized quadrature formula for stiffness matrix computation. Error estimates and stability analysis are provided, along with numerical experiments.
We present a novel Galerkin method for solving partial differential equations on the sphere. The problem is discretized by a highly localized basis which is easily constructed. The stiffness matrix entries are computed by a recently developed quadrature formula unique to the localized bases we consider. We present error estimates and investigate the stability of the discrete stiffness matrix. Implementation and numerical experiments are discussed.