Surface finite element approximation of parabolic SPDEs with Whittle--Matérn noise

We propose and analyse a new type of fully discrete surface finite element approximation of a class of linear parabolic stochastic evolution equations with additive noise. Our discretization uses a surface finite element approximation of the noise, and is tailored for equations with noise having covariance operator defined by (negative powers of) elliptic operators, like Whittle–Matérn random fields. We derive strong and pathwise convergence rates of our approximation, and verify these by numerical experiments.