Euler–Maruyama approximations of the stochastic heat equation on the sphere
Journal article, 2024

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.

Spectral approximation

Second moment

Euler–Maruyama scheme

Isotropic Wiener noise

Stochastic heat equation

Strong convergence

Stochastic evolution on surfaces


Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Ioanna Motschan-Armen

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Journal of Computational Dynamics

2158-2491 (ISSN) 2158-2505 (eISSN)

Vol. 11 1 23-42

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Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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