Approximation of the Lévy-driven stochastic heat equation on the sphere

The stochastic heat equation on the sphere driven by an additive square-integra-ble Lévy process is approximated by a spectral method in space and forward and backward Euler–Maruyama schemes in time. New regularity results are proven for its solution. The spectral approximation is based on a truncation of the series expansion with respect to the spherical harmonic functions. For a given regularity of the initial condition and two different settings of regularity for the driving noise, strong convergence rates for the spectral approximation and for the Euler–Maruyama methods are proven. Moreover, weak rates of up to twice the strong rates are shown. Numerical simulations confirm the theoretical results.