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We study a general class of singular degenerate parabolic stochastic partialdifferential equations (SPDEs) which include, in particular, the stochasticporous medium equations and the stochastic fast diffusion equation. We proposea fully discrete numerical approximation of the considered SPDEs based on thevery weak formulation. By exploiting the monotonicity properties of theproposed formulation we prove the convergence of the numerical approximationtowards the unique solution. Furthermore, we construct an implementable finiteelement scheme for the spatial discretization of the very weak formulation andprovide numerical simulations to demonstrate the practicability of the proposeddiscretization.

Numerical approximation of singular-degenerate parabolic stochastic PDEs