Finite element approximation of parabolic spdes with Whittle–Matérn noise

Journal article, 2026

We propose and analyze a new type of fully discrete finite element approximation of a class of linear stochastic parabolic evolution equations with additive noise. Our discretization differs from previous ones in that we use a finite element approximation of the noise, as opposed to an L² projection. This approximation is tailored for equations where the noise has covariance operator defined in terms of (negative powers of) elliptic operators, like Whittle–Matérn random fields. Strong convergence rates up to order 2 in space and 1 in time are shown and verified by numerical experiments in dimensions 1 and 2.