PSEUDODIFFERENTIAL EQUATIONS ON THE SPHERE WITH SPHERICAL SPLINES
T. D. Pham, Thanh Tran, Alexey Vyacheslavovich Chernov · Mathematical Models and Methods in Applied Sciences · 2011
Spherical splines 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 using Galerkin method. We prove optimal convergence (in Sobolev norms) of the approximate solution by spherical splines to the exact solution. Our numerical results underlie the theoretical result.