The gradient discretisation method (GDM) -- a generic framework encompassing many numerical methods -- is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by compactness method using discrete functional analysis tools, Skorohod theorem and the martingale representation theorem. The generic convergence results established in the GDM framework are applicable to a range of different numerical methods, including for example mass-lumped finite elements, but also some finite volume methods, mimetic methods, lowest-order virtual element methods, etc. Theoretical results are complemented by numerical tests based on two methods that fit in GDM framework.

翻译：梯度离散方法（GDM）——一种包含多种数值方法的通用框架——针对带有乘性噪声的一般随机Stefan问题进行了研究。通过使用离散泛函分析工具、Skorohod定理和鞅表示定理的紧致性方法，证明了数值解的收敛性。在GDM框架内建立的通用收敛结果适用于一系列不同的数值方法，例如包括集中质量有限元法，以及某些有限体积法、仿射方法、最低阶虚拟元方法等。理论结果通过两种符合GDM框架的方法的数值测试得到了补充。