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The stochastic heat equation on the sphere driven by additive isotropicWiener noise is approximated by a spectral method in space and forward andbackward Euler-Maruyama schemes in time. The spectral approximation is based ona truncation of the series expansion with respect to the spherical harmonicfunctions. Optimal strong convergence rates for a given regularity of theinitial condition and driving noise are derived for the Euler-Maruyama methods.Besides strong convergence, convergence of the expectation and second moment isshown, where the approximation of the second moment converges with twice thestrong rate. Numerical simulations confirm the theoretical results.

Euler-Maruyama approximations of the stochastic heat equation on the sphere