Strong convergence rates for full-discrete approximations of the stochastic Allen-Cahn equations on 2D torus
<|reference_start|>Strong convergence rates for full-discrete approximations of the stochastic Allen-Cahn equations on 2D torus: In this paper we construct space-time full discretizations of stochastic Allen-Cahn equations driven by space-time white noise on 2D torus. The approximations are implemented by tamed exponential Euler discretization in time and spectral Galerkin method in space. We finally obtain the convergence rates with the spatial order of $\alpha-\delta$ and the temporal order of ${\alpha}/{6}-\delta$ in $\mathcal C^{-\alpha}$ for $\alpha\in(0,1/3)$ and $\delta>0$ arbitrarily small.<|reference_end|>
@article{ma2024strong,
    title={Strong convergence rates for full-discrete approximations of the
  stochastic Allen-Cahn equations on 2D torus},
    author={Ting Ma, Lifei Wang, Huanyu Yang},
    journal={arXiv preprint arXiv:2406.03715},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.03715},
    primaryClass={math.PR cs.NA math.NA}
}