Weak Convergence of Finite Element Method for Stochastic Elastic Equation Driven By Additive Noise |
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Authors: | Ruisheng Qi Xiaoyuan Yang |
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Affiliation: | 1. Department of Mathematics, LMIB of the Ministry of Education, Beihang University, Beijing, 100191, China
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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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