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arXiv · 2501.18240

Numerical approximation of nonlinear fourth-order SPDEs with additive space-time white noise

Dirk Blömker·Chengcheng Ling·Johannes Rimmele
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Abstract

We consider the strong numerical approximation for a fourth-order stochastic nonlinear SPDE driven by space-time white noise on {$d=1,2,3$}-dimensional torus. We consider its full discretisation with a spectral Galerkin scheme in space and Euler scheme in time. We show the convergence with almost spatial rate $2-\frac{d}{2}$ and $\frac{6-d}{4}$-temporal rate obtained mainly via \it{Stochastic Sewing} technique.

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Dirk Blömker, Chengcheng Ling, Johannes Rimmele. 2026-08-05. Numerical approximation of nonlinear fourth-order SPDEs with additive space-time white noise. https://arxiv.org/abs/2501.18240

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