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

Abstract: The stochastic heat equation on the sphere driven by additive isotropic Wiener noise is approximated by a spectral method in space and forward and backward Euler– Maruyama schemes in time. The spectral approximation is based on a truncation of the series expansion with respect to the spherical harmonic functions. Optimal strong convergence rates for a given regularity of the initial condition and driving noise are derived for the Euler– Maruyama methods. Besides strong convergence, convergence of the expectation and second moment is shown, where the approximation of the second moment converges with twice the strong rate. Numerical simulations confirm the theoretical results. This is joint work with Annika Lang.

numerical analysisoptimization and control

Audience: researchers in the topic

( paper )

CAM seminar

Series comments: Online streaming via zoom on exceptional cases if requested. Please contact the organizers at the latest Monday 11:45.