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

Xiaoyuan Yang ,  Xiaocui Li ,  Ruisheng Qi and Yinghan Zhang

10.4208/jcm.1506-m2014-0186

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

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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.

  • History

Published online: 2015-10

  • AMS Subject Headings

60H15, 65M60.

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