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arXiv · 2512.17712

Study of a TPFA scheme for the stochastic Allen-Cahn problem with constraint through numerical experiments

Niklas Sapountzoglou·Aleksandra Zimmermann
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Abstract

This contribution provides numerical experiments for a finite volume scheme for an approximation of the stochastic Allen-Cahn equation with homogeneous Neumann boundary conditions. The approximation is done by a Yosida approximation of the subdifferential operator. The problem is set on a polygonal bounded domain in two or three dimensions. The non-linear character of the projection term induces challenges to implement the scheme. To this end, we provide a splitting method for the finite volume scheme. We show that the splitting method is accurate. The computational error estimates induce that the squared $L^2$-error w.r.t. time is of order $1$ as long as the noise term is small enough. For larger noise terms the order of convergence w.r.t. time might become worse.

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Niklas Sapountzoglou, Aleksandra Zimmermann. 2025-12-19. Study of a TPFA scheme for the stochastic Allen-Cahn problem with constraint through numerical experiments. https://arxiv.org/abs/2512.17712

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