Quadrature finite element method for elliptic eigenvalue problems
type: Item
instance of: scholarly article
title: Quadrature finite element method for elliptic eigenvalue problems
zbMATH Open document ID: 1379.65086
DOI: 10.1134/S1995080217050341
author: S. I. Solov'ev
published in: Lobachevskii Journal of Mathematics
publication date: 2017-12-06T00:00:00Z
review text: The author considers a positive semi-definite eigenvalue problem for second-order self-adjoint elliptic differential operators with Dirichlet boundary conditions which is posed on a bounded domain in two dimensions with smooth boundary. The stated problem has a nondecreasing sequence of positive eigenvalues of finite multiplicity with a limit point at infinity. To the sequence of eigenvalues, there corresponds an orthonormal system of eigenfunctions. A finite element method with numerical integration and Lagrange curved triangular finite elements of arbitrary order is applied. Error estimates for approximate eigenvalues and eigenfunctions are proved.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 6815761
zbMATH Keywords: eigenfunction
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: finite element method
zbMATH Keywords: curved finite element
zbMATH Keywords: quadrature formula
zbMATH Keywords: numerical integration
zbMATH Keywords: error estimates
zbMATH Keywords: second-order self-adjoint elliptic differential operator
describes a project that uses: NLEVP
MaRDI profile type: Publication
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full work available at URL: s1995080217050341
OpenAlex ID: W2755193708
description: scientific article; zbMATH DE number 6815761