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, Skorokhod 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.

中文翻译：

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随机Stefan问题的数值分析


梯度离散方法（GDM）——一个包含许多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。利用离散泛函分析工具、Skorokhod 定理和鞅表示定理，通过紧致性方法证明了数值解的收敛性。 GDM 框架中建立的通用收敛结果适用于一系列不同的数值方法，包括质量集总有限元，但也适用于一些有限体积方法、拟态方法、最低阶虚拟元素方法等。理论结果为并辅以基于两种适合 GDM 框架的方法的数值测试。