Abstract We consider the stochastic Cahn–Hilliard equation with additive space–time white noise ^ Ẇ in dimension d=2, 3, where 0 is an interfacial width parameter. We study a numerical approximation of the equation that 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 that is robust with respect to the inverse of the interfacial width parameter. Furthermore, by a splitting approach we show that for sufficiently large scaling parameter the numerical approximation of the stochastic Cahn–Hilliard equation converges uniformly to the deterministic Hele-Shaw/Mullins–Sekerka problem in the sharp-interface limit 0.
Baňas et al. (Tue,) studied this question.