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 - <p style="text-align: justify;">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 &quot;Green&#39;s method&quot; 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.</p>