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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