Year: 2015
Author: Xiaoyuan Yang, Xiaocui Li, Ruisheng Qi, Yinghan Zhang
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 533–556
Abstract
This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity, we rewrite the two types of stochastic hyperbolic equations into a unified form. We convert the stochastic hyperbolic equation into a regularized equation by discretizing the white noise and then consider the full-discrete finite element method for the regularized equation. We derive the modeling error by using "Green's method" and the finite element approximation error by using the error estimates of the deterministic equation. Some numerical examples are presented to verify the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1506-m2014-0186
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 5 : pp. 533–556
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Stochastic hyperbolic equation Strong convergence Additive noise Wiener process.