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Volume 33, Issue 5
Full-Discrete Finite Element Method for Stochastic Hyperbolic Equation

Xiaoyuan Yang, Xiaocui Li, Ruisheng Qi & Yinghan Zhang

DOI: 10.4208/jcm.1506-m2014-0186

J. Comp. Math., 33 (2015), pp. 533-556.

Published online: 2015-10

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  • 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.

  • Keywords

Stochastic hyperbolic equation, Strong convergence, Additive noise, Wiener process.

  • AMS Subject Headings

60H15, 65M60.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiaoyuanyang@vip.163.com (Xiaoyuan Yang)

anny9702@126.com (Xiaocui Li)

qiruisheng123@sohu.com (Ruisheng Qi)

zhangyinghan007@126.com (Yinghan Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-533, author = {Yang , XiaoyuanLi , XiaocuiQi , Ruisheng and Zhang , Yinghan}, title = {Full-Discrete Finite Element Method for Stochastic Hyperbolic Equation}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1506-m2014-0186}, url = {http://global-sci.org/intro/article_detail/jcm/9858.html} }
TY - JOUR T1 - Full-Discrete Finite Element Method for Stochastic Hyperbolic Equation AU - Yang , Xiaoyuan AU - Li , Xiaocui AU - Qi , Ruisheng AU - Zhang , Yinghan JO - Journal of Computational Mathematics VL - 5 SP - 533 EP - 556 PY - 2015 DA - 2015/10 SN - 33 DO - http://doi.org/10.4208/jcm.1506-m2014-0186 UR - https://global-sci.org/intro/article_detail/jcm/9858.html KW - Stochastic hyperbolic equation, Strong convergence, Additive noise, Wiener process. AB -

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.

Yang , XiaoyuanLi , XiaocuiQi , Ruisheng and Zhang , Yinghan. (2015). Full-Discrete Finite Element Method for Stochastic Hyperbolic Equation. Journal of Computational Mathematics. 33 (5). 533-556. doi:10.4208/jcm.1506-m2014-0186
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