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
In this paper we proceed with the multiscale analysis of semilinear damped stochastic wave motions. The analysis is made by combining the well-known sigma convergence method with its stochastic counterpart, associated...In this paper we proceed with the multiscale analysis of semilinear damped stochastic wave motions. The analysis is made by combining the well-known sigma convergence method with its stochastic counterpart, associated to some compactness results such as the Prokhorov and Skorokhod theorems. We derive the equivalent model, which is of the same type as the micro-model. One of the novelties of the work is that the corrector problem is solved in the classical sense of distributions,thereby allowing numerical computations of the homogenized coefficients.展开更多
For a family of linear hyperbolic damped stochastic wave equations with rapidly oscillating coefficients, we establish the homogenization result by using the sigma-convergence method. This is achieved under an abstrac...For a family of linear hyperbolic damped stochastic wave equations with rapidly oscillating coefficients, we establish the homogenization result by using the sigma-convergence method. This is achieved under an abstract assumption covering special cases like the periodicity, the almost periodicity and some others.展开更多
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.
文摘In this paper we proceed with the multiscale analysis of semilinear damped stochastic wave motions. The analysis is made by combining the well-known sigma convergence method with its stochastic counterpart, associated to some compactness results such as the Prokhorov and Skorokhod theorems. We derive the equivalent model, which is of the same type as the micro-model. One of the novelties of the work is that the corrector problem is solved in the classical sense of distributions,thereby allowing numerical computations of the homogenized coefficients.
基金the support of the CETIC(African Center of Excellence in Information and Communication Technologies)the support of the Humboldt Foundation
文摘For a family of linear hyperbolic damped stochastic wave equations with rapidly oscillating coefficients, we establish the homogenization result by using the sigma-convergence method. This is achieved under an abstract assumption covering special cases like the periodicity, the almost periodicity and some others.
