Pseudodifferential equations on the sphere with radial basis functions: Error analysis
نویسندگان
چکیده
Spherical radial basis functions are used to define approximate solutions to strongly elliptic and elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and collocation methods. A salient feature of the paper is a unified theory for error analysis of both approximation methods.
منابع مشابه
Strongly elliptic pseudodifferential equations on the sphere with radial basis functions
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and collocation methods. A salient feature of the paper is a unified theory for error analysis of both approximation methods.
متن کاملCollocation Solutions to Pseudodifferential Equations of Negative Orders on the Sphere Using Spherical Radial Basis Functions
Abstract. Spherical radial basis functions are used to define approximate solutions to pseudodifferential equations of negative orders on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the collocation method. A salient feature of our approach in this paper is a simple error analysis for the collocation method using the same argument as that for the G...
متن کاملPreconditioners for pseudodifferential equations on the sphere with radial basis functions
In a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the Galerkin approximation of elliptic partial differential equations on the sphere. In this paper the methods are extended to more general pseudodifferential equations on the sphere, using as before spherical radial basis functions for the approximation space, and again preconditioning the i...
متن کاملBoundary Integral Equations on the Sphere with Radial Basis Functions: Error Analysis
Radial basis functions are used to define approximate solutions to boundary integral equations on the unit sphere. These equations arise from the integral reformulation of the Laplace equation in the exterior of the sphere, with given Dirichlet or Neumann data, and a vanishing condition at infinity. Error estimates are proved. Numerical results supporting the theoretical results are presented.
متن کاملSolving parabolic equations on the unit sphere via Laplace transforms and radial basis functions
We propose a method to construct numerical solutions of parabolic equations on the unit sphere. The time discretization uses Laplace transforms and quadrature. The spatial approximation of the solution employs radial basis functions restricted to the sphere. The method allows us to construct high accuracy numerical solutions in parallel. We establish L2 error estimates for smooth and nonsmooth ...
متن کامل