We derive a posteriori error estimates for a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation. The a posteriori bound is obtained by a splitting of the equation into a linear stochastic partial differential equation (SPDE) and a nonlinear random partial differential equation (RPDE). The resulting estimate is robust with respect to the interfacial width parameter and is computable since it involves the discrete principal eigenvalue of a linearized (stochastic) Cahn-Hilliard operator. Furthermore, the estimate is robust with respect to topological changes as well as the intensity of the stochastic noise. We provide numerical simulations to demonstrate the practicability of the proposed adaptive algorithm.

翻译：我们得出了完全离散的卡赫-希利亚德方程式的有限元素近似值的事后误差估计值; 后缘约束值是通过将方程式分成线性随机部分差分方程和非线性随机部分差分方程(RPDE)获得的; 由此得出的估计值对间宽度参数来说是稳健的, 可以计算, 因为它涉及线性(随机)卡赫- 希利亚德操作员的离散主要电子元值; 此外, 该估计值对地形变化和随机噪声强度而言是稳健的; 我们提供数字模拟,以显示拟议的适应算法的实用性。