广义随机变量抛物型随机偏微分方程有限元近似的先验误差估计

Pub Date : 2015-02-19 DOI:10.1080/17442508.2014.989526

Christophe Audouze, P. Nair

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引用次数: 0

摘要

我们考虑了抛物型随机偏微分方程(SPDEs)的有限元近似与加权时间离散方案。本文研究了数值格式的稳定性，并利用Galvis和Sarkis[近似无均匀椭圆的无限维随机达西方程，SIAM J. number]的结果提供了一个先验误差估计。论椭圆型SPDEs [j] .学报，47(5)(2009)，pp. 3624-3651。

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A priori error estimates for finite element approximations of parabolic stochastic partial differential equations with generalized random variables

We consider finite element approximations of parabolic stochastic partial differential equations (SPDEs) in conjunction with the -weighted temporal discretization scheme. We study the stability of the numerical scheme and provide a priori error estimates, using a result of Galvis and Sarkis [Approximating infinity-dimensional stochastic Darcy's equations without uniform ellipticity, SIAM J. Numer. Anal. 47(5) (2009), pp. 3624–3651] on elliptic SPDEs.

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