论文标题
奇异抛物线随机PDE的数值近似
Numerical approximation of singular-degenerate parabolic stochastic PDEs
论文作者
论文摘要
我们研究了一类奇异抛物性抛物线随机部分微分方程（SPDE）的一般类别，其中包括随机多孔培养基方程和随机快速扩散方程。我们根据非常弱的公式提出了对所考虑的SPDE的完全离散的数值近似。通过利用所提出的公式的单调性特性，我们证明了数值近似向独特溶液的收敛性。此外，我们为非常弱的公式的空间离散化构建了可实施的有限元方案，并提供了数值模拟，以证明提议的离散化的实用性。
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.
