2024/12/17 by Jianbo Cui, Cui, Jianbo, Feng‐Yu Wang +1 · 1 citation
Computer Science · #Advanced Mathematical Modeling in Engineering
paper · pdf · doi:10.48550/arxiv.2412.12604
In the study of geometric surface evolutions, stochastic reaction-diffusion equation provides a powerful tool for capturing and simulating complex dynamics. A critical challenge in this area is developing numerical approximations that exhibit error bounds with polynomial dependence on \vv-1, where the small parameter \vv>0 represents the diffuse interface thickness. The existence of such bounds for fully discrete approximations of stochastic reaction-diffusion equations remains unclear in the literature. In this work, we address this challenge by leveraging the asymptotic log-Harnack inequality to overcome the exponential growth of \vv-1. Furthermore, we establish the numerical weak error bounds under the truncated Wasserstein distance for the spectral Galerkin method and a fully discrete tamed Euler scheme, with explicit polynomial dependence on \vv-1.