一类随机非自伴波方程的半离散有限元近似

doi:10.12286/jssx.2017.1.42

计算数学 ›› 2017, Vol. 39 ›› Issue (1): 42-58.DOI: 10.12286/jssx.2017.1.42

一类随机非自伴波方程的半离散有限元近似

李晓翠¹, 杨小远¹, 张英晗²

1. 北京航空航天大学数学与系统科学学院, 北京 100191;
2. 北京科技大学数理学院, 北京 100083

收稿日期:2015-12-30 出版日期:2017-02-15 发布日期:2017-02-17
基金资助:
国家自然科学基金（61271010），北京市自然科学基金（4152029）资助项目.

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李晓翠, 杨小远, 张英晗. 一类随机非自伴波方程的半离散有限元近似[J]. 计算数学, 2017, 39(1): 42-58.

Li Xiaocui, Yang Xiaoyuan, Zhang Yinghan. SEMIDISCRETE FINITE ELEMENT APPROXIMATION OF STOCHASTIC NONSELFADJOINT WAVE EQUATION[J]. Mathematica Numerica Sinica, 2017, 39(1): 42-58.

SEMIDISCRETE FINITE ELEMENT APPROXIMATION OF STOCHASTIC NONSELFADJOINT WAVE EQUATION

Li Xiaocui¹, Yang Xiaoyuan¹, Zhang Yinghan²

1. Department of Mathematics, Beihang University, LMIB of the Ministry of Education, Beijing 100191, China;
2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received:2015-12-30 Online:2017-02-15 Published:2017-02-17

本文研究了由白噪音驱动的随机非自伴波方程的有限元近似，由于线性算子A非自伴，不能应用A的特征值和特征向量，从而得到的结果更具有一般性.空间离散上采用标准的有限元法，并借助强连续算子函数的性质，得到了该方程的强收敛误差估计.本文方法也适用于多维情况的分析.最后用数值算例验证了理论分析的正确性.

关键词： 随机非自伴波方程, 有限元方法, 非自伴算子, cosine算子函数, 强收敛

We study the semidiscrete finite element approximation of the linear stochastic nonselfadjoint wave equation forced by additive noise.The results here are more general since the linear operator A does not need to be self-adjoint and we do not need information about eigenvalues and eigenfunctions of the linear operator A.In order to obtain the strong convergence error estimates,a standard finite element method for the spatial discretisation and the properties of a strongly continuous operator cosine function are used.The error estimates are applicable in the multi-dimensional case.

Key words: stochastic nonselfadjoint wave equation, finite element method, nonselfadjoint operator, cosine operator function, strong convergence

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摘要

一类随机非自伴波方程的半离散有限元近似

SEMIDISCRETE FINITE ELEMENT APPROXIMATION OF STOCHASTIC NONSELFADJOINT WAVE EQUATION

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