  We study a general class of singular degenerate parabolic stochastic partial
differential equations (SPDEs) which include, in particular, the stochastic
porous medium equations and the stochastic fast diffusion equation. We propose
a fully discrete numerical approximation of the considered SPDEs based on the
very weak formulation. By exploiting the monotonicity properties of the
proposed formulation we prove the convergence of the numerical approximation
towards the unique solution. Furthermore, we construct an implementable finite
element scheme for the spatial discretization of the very weak formulation and
provide numerical simulations to demonstrate the practicability of the proposed
discretization.
