Solving 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 $L_2$ error estimates for smooth and nonsmooth initial data, and describe some numerical experiments. 
Q. T. Le Gia and William McLean
math.NA