Least squares h-p spectral element method for elliptic eigenvalue problems

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• 作者：Lokendra K. Balyan^a ; ^{balyan@iiitdmj.ac.in} ; ^{lokendra.balyan@gmail.com} ; Pravir K. Dutt^b ; ^{pravir@iitk.ac.in} ; R.K.S. Rathore^b ; ^{rksr@iitk.ac.in}
• 关键词：Approximation of eigenvalues and eigenvectors ; Stability estimates ; h-p spectral element method ; Singularities ; Exponential accuracy ; Arnoldi method
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 June, 2012
• 卷：218
• 期：19
• 页码：9596-9613
• 文件大小：718 K

摘要

In this paper we discuss how to solve elliptic eigenvalue problems on polygonal domains using least squares methods. Exponential rate of convergence has been obtained for approximate eigenvalues as well as the eigenfunctions. The result is proved when the boundary of underlying domain is smooth and also when the boundary contains corners. The computational results confirm the error estimates. The results proved in the paper are valid for multiple or clustered eigenvalues also. The method works for non-self adjoint problems too.