Numerical approximation of singular-degenerate parabolic stochastic PDEs
- Authors: Ľubomír Baňas, Benjamin Gess, Christian Vieth
- Preprint year: 2020
- First public date: 2020-12-22
- arXiv: 2012.12150
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: IMA journal of numerical analysis, 44 (2024) 4, pp. 2090-2137
- DOI: 10.1093/imanum/drad061
Abstract
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.