  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.
