Approximation of parabolic PDEs on spheres using spherical basis functions (Q1774027)

The author investigates the approximate solution of the heat equation on the \(m\)-dimensional sphere using reproducing kernel Hilbert spaces and spherical harmonics as basis functions. For the discretization, a general system of pairwise different collocation points on the sphere is used. Stability and error estimates are derived for the semidiscrete problem, assuming appropriate smoothness of the data. For the full discretization, both the backward Euler and Crank-Nicolson schemes are considered, and numerical experiments are reported for the backward Euler scheme.