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

2025/10/09 by Auestad, Øyvind Stormark, Fuglstad, Geir-Arne, Lang, Annika
#35K10 #35K51 #60H15 #65C20 #65C30 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.08443

Abstract

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.

Citations

• Numerical approximation of linear parabolic evolution equations revisited
• Numerical Approximation of Gaussian random fields on Closed Surfaces
• A diffusion-based spatio-temporal extension of Gaussian Matérn fields
• On Sinc Quadrature Approximations of Fractional Powers of Regularly\n Accretive Operators
• A non-uniform discretization of stochastic heat equations with\n multiplicative noise on the unit sphere

Cited by

• Approximation of the Lévy-driven stochastic heat equation on the sphere

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