# Nonnegativity preserving convergent schemes for stochastic porous-medium equations

@article{Grillmeier2019NonnegativityPC, title={Nonnegativity preserving convergent schemes for stochastic porous-medium equations}, author={Hubertus Grillmeier and G{\"u}nther Gr{\"u}n}, journal={Math. Comput.}, year={2019}, volume={88}, pages={1021-1059} }

We propose a fully discrete finite-element scheme for stochastic porousmedium equations with linear, multiplicative noise given by a source term. A subtle discretization of the degenerate diffusion coefficient combined with a noise approximation by bounded stochastic increments permits us to prove H1-regularity and nonnegativity of discrete solutions. By Nikolsk’ii estimates in time, Skorokhod-type arguments and the martingale representation theorem, convergence of appropriate subsequences…

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