论文标题
Leray-Lions操作员的随机演化方程的数值方法的设计和收敛分析
Design and convergence analysis of numerical methods for stochastic evolution equations with Leray-Lions operator
论文作者
论文摘要
*梯度离散方法（GDM）是一个通用框架，涵盖许多经典方法（有限元素，有限体积，不连续的Galerkin等），用于设计和分析扩散模型的数值方案。在本文中，我们研究了基于Leray-Lions型操作员的一般随机演化问题的GDM。该问题包含随机$ p $ -laplace方程作为特定情况。通过使用离散功能分析技术，Skorohod定理和Kolmogorov检验证明了梯度方案（GS）溶液的收敛性。特别是，我们为问题提供了一个独立的证据，证明了Martingale解决方案的存在。这样，我们奠定了基础并提供了证明GS近似随机部分微分方程的收敛技术。
*The gradient discretisation method (GDM) is a generic framework, covering many classical methods (Finite Elements, Finite Volumes, Discontinuous Galerkin, etc.), for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for a general stochastic evolution problem based on a Leray--Lions type operator. The problem contains the stochastic $p$-Laplace equation as a particular case. The convergence of the Gradient Scheme (GS) solutions is proved by using Discrete Functional Analysis techniques, Skorohod theorem and the Kolmogorov test. In particular, we provide an independent proof of the existence of weak martingale solutions for the problem. In this way, we lay foundations and provide techniques for proving convergence of the GS approximating stochastic partial differential equations.
