We consider the stochastic Cahn-Hilliard equation with additive space-time white noise $\epsilon^{\gamma}\dot{W}$ in dimension $d=2,3$, where $\epsilon>0$ is an interfacial width parameter. We study numerical approximation of the equation which combines a structure preserving implicit time-discretization scheme with a discrete approximation of the space-time white noise. We derive a strong error estimate for the considered numerical approximation which is robust with respect to the inverse of the interfacial width parameter $\epsilon$. Furthermore, by a splitting approach, we show that for sufficiently large scaling parameter $\gamma$, the numerical approximation of the stochastic Cahn-Hilliard equation converges uniformly to the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp interface limit $\epsilon\rightarrow 0$.

翻译：我们考虑带有附加时空白噪声$\epsilon^{\gamma}\dot{W}$的随机Cahn-Hilliard方程，其中维数$d=2,3$，$\epsilon>0$为界面宽度参数。我们研究该方程的数值近似方法，该方法结合了结构保持隐式时间离散格式与时空白噪声的离散近似。我们推导了所考虑的数值近似的强误差估计，该估计对于界面宽度参数$\epsilon$的倒数具有稳健性。此外，通过分裂方法，我们证明对于足够大的尺度参数$\gamma$，随机Cahn-Hilliard方程的数值近似在尖锐界面极限$\epsilon\rightarrow 0$下一致收敛于确定性Hele-Shaw/Mullins-Sekerka问题。