Abstract

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 algebraic dependence on the inverse diffuse interface thickness which blows up near the sharp interface. 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, and further establish the numerical weak error bounds under the truncated Wasserstein distance for the discrete tamed Euler scheme. This is a joint work with Jianbo Cui (Hong Kong Polytech. Uni.).