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Weak Convergence of Finite Element Method for Stochastic Elastic Equation Driven By Additive Noise

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Abstract

In this paper we study the weak convergence of the semidiscrete and full discrete finite element methods for the stochastic elastic equation driven by additive noise, based on \(C^0\) or \(C^1\) piecewise polynomials. In order to simplify the analysis of weak convergence, we rewrite the stochastic elastic equation in an abstract problem and the solutions of the semidiscrete and full discrete problems in a unified form. We obtain that the weak order is twice the strong order, both in time and in space. Numerical experiments are carried out to verify the theoretical results.

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Acknowledgments

The author thanks the anonymous referees whose constructive criticism helped improve this article. This research was supported the National Key Basic Research Program (973) of China under Grant 2009CB724001 and National Natural Science Foundation of China under Grant 61271010.

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  1. Department of Mathematics, LMIB of the Ministry of Education, Beihang University, Beijing, 100191, China

    Ruisheng Qi & Xiaoyuan Yang

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  1. Ruisheng Qi
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  2. Xiaoyuan Yang
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Correspondence to Xiaoyuan Yang.

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Qi, R., Yang, X. Weak Convergence of Finite Element Method for Stochastic Elastic Equation Driven By Additive Noise. J Sci Comput 56, 450–470 (2013). https://doi.org/10.1007/s10915-013-9683-2

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