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arXiv · 2510.08443

Surface finite element approximation of parabolic SPDEs with Whittle--Mat\'ern noise

Øyvind Stormark Auestad·Geir-Arne Fuglstad·Annika Lang
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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--Mat\'ern random fields. We derive strong and pathwise convergence rates of our approximation, and verify these by numerical experiments.

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Øyvind Stormark Auestad, Geir-Arne Fuglstad, Annika Lang. 2025-10-09. Surface finite element approximation of parabolic SPDEs with Whittle--Mat\'ern noise. https://arxiv.org/abs/2510.08443

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