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arXiv · 2608.28727

Overcoming the spatial order barrier for nonlinear SPDEs with additive space-time white noise

Lukas Anzeletti·Máté Gerencsér·Helena Kremp
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Abstract

We introduce a fully discrete numerical scheme for semilinear SPDEs with additive space-time white noise that overcomes the previous order barrier for the spatial convergence rate. The scheme achieves a strong convergence rate of $M^{-1+ε}$ in time and $N^{-3/2+ε}$ in space for any $ε>0$, where $M^{-1}$ and $N^{-1}$ are the temporal, respectively the spatial, meshsizes. This substantially improves the standard spatial error bounds of order $N^{-1/2}$ in the literature.

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Lukas Anzeletti, Máté Gerencsér, Helena Kremp. 2026-08-28. Overcoming the spatial order barrier for nonlinear SPDEs with additive space-time white noise. https://arxiv.org/abs/2608.28727

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