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Full-Discrete Finite Element Method for Stochastic Hyperbolic Equation

Full-Discrete Finite Element Method for Stochastic Hyperbolic Equation
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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.

Author Details

Xiaoyuan Yang

Xiaocui Li

Ruisheng Qi

Yinghan Zhang

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