An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative

In this paper, we propose a local discontinuous Galerkin (LDG) method forthe multi-dimensional stochastic Cahn-Hilliard type equation in a general form, whichinvolves second-order derivative $∆u$ in the multiplicative noise. The stability of ourscheme is proved for arbitrary polygonal domain with triangular meshes. We get thesub-optimal error estimate $mathbb{O}(h^k)$ if the Cartesian meshes with $Q^k$ elements are used.Numerical examples are given to display the performance of the LDG method.