凹角域上本征值有限元外推  

An Extrapolation Scheme for Finite Element Eigenvalues on Domains with Reentrant Corners

作　　者：杨一都[1] 罗贤兵[1] 

机构地区：[1]贵州师范大学数学系,贵阳550001

出　　处：《工程数学学报》2004年第F12期61-66,共6页Chinese Journal of Engineering Mathematics

基　　金：贵州省科委科学技术基金资助项目

摘　　要：H.Blum和R.Rannacher在完全合理的光滑性假设下,证明了凹角域上线性有限元本征值外推可达o(h2)精度阶。在此B-R方案基础上本文给出了一个新方案:1在粗网格上求一个逼λ的本征值λH:2在细网格上求一个线性代数方程组的解uhs,计算uhs的Rayleigh商:3外推。理论分析和数值实验都表明新方案达到了B-R方案的精度阶o(h2),且计算量成倍减少,更重要的是实施起来十分容易。工程力学界常常致需求最小本征值,这时本文方案的优越性特别明显。H.Blum and R.Rannacher, under suitable assumptions on smoothness, proved a rate of o(h2) for the extrapolation of finite element eigenvalues on domains with reentrant corners. Based on this, our paper constructs a new scheme, which yields an accuracy of o(h2). First, to solve an eigenvalue problem obtainsλH approximating A on the initial mesh; Then, solving a linear algebra equations derives uhs, and computing the quotient of ush obtains λs on the refined mesh; At last, extrapolate for λH and λs. Numerical experiments, confirming the theoretical rates of convergence, are presented. Computation is half of the other's, and employing the scheme is very easy. The minimum eigenvalue is often used in engineering and mechanics, when the advantage is obvious.

关 键 词：本征值 凹角域 光滑性 外推 线性代数方程组 数值实验 计算量 新方案 需求 理论分析 

分 类 号：O241.82[理学—计算数学] O413.1[理学—数学]