Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise
<|reference_start|>Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise: This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization uses the Euler scheme for temporal discretization and the finite element method for spatial discretization. A key contribution of this work is the introduction of a novel stability estimate for a discrete stochastic convolution, which plays a crucial role in establishing pathwise uniform convergence estimates for fully discrete approximations of nonlinear stochastic parabolic equations. By using this stability estimate in conjunction with the discrete stochastic maximal $L^p$-regularity estimate, the study derives a pathwise uniform convergence rate that encompasses general general spatial $L^q$-norms. Moreover, the theoretical convergence rate is verified by numerical experiments.<|reference_end|>
@article{li2024pathwise,
    title={Pathwise uniform convergence of a full discretization for a
  three-dimensional stochastic Allen-Cahn equation with multiplicative noise},
    author={Binjie Li and Qin Zhou},
    journal={arXiv preprint arXiv:2405.03016},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.03016},
    primaryClass={math.NA cs.NA}
}