Optimal Error Estimates of a Discontinuous Galerkin Method for Stochastic Allen-Cahn Equation Driven by Multiplicative Noise (Communications in Computational Physics, 2024)
In this paper, we develop and analyze an efficient discontinuous Galerkinmethod for stochastic Allen-Cahn equation driven by multiplicative noise. The proposed method is realized by symmetric interior penalty discontinuous Galerkin finiteelement method for space domain and implicit Euler method for time domain. Several new estimates and techniques are developed. Under some suitable regularity assumptions, we rigorously establish strong convergence results for the proposed fullydiscrete numerical scheme and obtain optimal convergence rates in both space andtime. Numerical experiments are also carried out to validate our theoretical resultsand demonstrate the effectiveness of the proposed method.