  *The gradient discretisation method (GDM) is a generic framework, covering
many classical methods (Finite Elements, Finite Volumes, Discontinuous
Galerkin, etc.), for designing and analysing numerical schemes for diffusion
models. In this paper, we study the GDM for a general stochastic evolution
problem based on a Leray--Lions type operator. The problem contains the
stochastic $p$-Laplace equation as a particular case. The convergence of the
Gradient Scheme (GS) solutions is proved by using Discrete Functional Analysis
techniques, Skorohod theorem and the Kolmogorov test. In particular, we provide
an independent proof of the existence of weak martingale solutions for the
problem. In this way, we lay foundations and provide techniques for proving
convergence of the GS approximating stochastic partial differential equations.
