Numerical analysis of a full discretization for stochastic Cahn--Hilliard equation driven by additive noise

Abstract

In this article, we consider the stochastic Cahn--Hilliard equation driven by space-time white noise. We discretize this equation by using a spatial spectral Galerkin method and a temporal accelerated implicit Euler method. The optimal regularity properties and uniform moment bounds of the exact and numerical solutions are shown. Then we prove that the proposed numerical method is strongly convergent with the sharp convergence rate in a negative Sobolev space. By using an interpolation approach, we deduce the spatial optimal convergence rate and the temporal super-convergence rate of the proposed numerical method in strong convergence sense. To the best of our knowledge, this is the first result on the strong convergence rates of numerical methods for the stochastic Cahn--Hilliard equation driven by space-time white noise. This interpolation approach is also applied to the general noise and high dimension cases, and strong convergence rate results of the proposed scheme are given.

arXiv comment31 pages

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Cited by in corpus (6)

• Weak convergence and invariant measure of a full discretization for non-globally Lipschitz parabolic SPDE
• Error estimates of semi-discrete and fully discrete finite element methods for the Cahn-Hilliard-Cook equation
• Energy-preserving exponential integrable numerical method for stochastic cubic wave equation with additive noise
• Wellposedness and regularity estimate for stochastic Cahn--Hilliard equation with unbounded noise diffusion
• Strong and weak convergence rates of finite element method for stochastic partial differential equation with non-sided Lipschitz coefficient
• Absolute continuity and numerical approximation of stochastic Cahn--Hilliard equation with unbounded noise diffusion