An explicit differencescheme is described,analyzed and tested for numer-ically approximating stochastic elastic equation driven by infinite dimensional noise.The noise processes are approximated by piecewise constant ...An explicit differencescheme is described,analyzed and tested for numer-ically approximating stochastic elastic equation driven by infinite dimensional noise.The noise processes are approximated by piecewise constant random processes and the integral formula of the stochastic elastic equation is approximated by a truncated series.Error analysis of the numerical method yields estimate of convergence rate.The rate of convergence is demonstrated with numerical experiments.展开更多
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 hype...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.展开更多
基金supported by the Innovation Foundation of BUAA for PhD Graduates and the National Natural Science Foundation of China under grant 61271010.
文摘An explicit differencescheme is described,analyzed and tested for numer-ically approximating stochastic elastic equation driven by infinite dimensional noise.The noise processes are approximated by piecewise constant random processes and the integral formula of the stochastic elastic equation is approximated by a truncated series.Error analysis of the numerical method yields estimate of convergence rate.The rate of convergence is demonstrated with numerical experiments.
基金The authors would like to express their sincere gratitude to the anony- mous reviewers for their careful reading of the manuscript, as well as their comments that lead to a considerable improvement of the original manuscript. The first author was supported by the National Natural Science Foundation of China under grant 61271010 and by Beijing Natural Science Foundation under grant 4152029.
文摘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.
