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

Pub Date : 2015-02-19 DOI:10.1080/17442508.2014.989526
Christophe Audouze, P. Nair
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Abstract

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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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
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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