STRONG CONVERGENCE OF FULL DISCRETIZATION FOR STOCHASTIC CAHN-HILLIARD EQUATION DRIVEN BY ADDITIVE NOISE

In this article, we consider the stochastic Cahn-Hilliard equation driven by additive noise. We discretize the equation by exploiting the spectral Galerkin method in space and a temporal accelerated implicit Euler method. Based on optimal regularity estimates of both exact and numerical solutions, we prove that the proposed numerical method is strongly convergent with a sharp convergence rate in a negative Sobolev space. Utilizing the semigroup theory and interpolation inequality, we deduce the spatial optimal convergence rate and the temporal superconvergence rate of the proposed numerical method in the strong sense.

Automated summary

In this article, the stochastic Cahn-Hilliard equation is discretized using the spectral Galerkin method in space and a temporally accelerated implicit Euler method. The proposed numerical method is proven to have strong convergence with a sharp convergence rate in a negative Sobolev space. By utilizing semigroup theory and interpolation inequality, the spatial optimal convergence rate and temporal superconvergence rate of the numerical method in the strong sense are deduced.