On the numerical approximation of some types of nonstandard second-order eigenvalue problems for vector value functions
type: Item
instance of: scholarly article
title: On the numerical approximation of some types of nonstandard second-order eigenvalue problems for vector value functions
zbMATH Open document ID: 0951.65110
DOI: 10.1016/S0377-0427(99)00122-3
published in: Journal of Computational and Applied Mathematics
publication date: 2000-06-07T00:00:00Z
review text: The authors study finite element approximation methods for some types of second-order elliptic eigenvalue problems (EVPs) for vector-valued functions on a convex polygonal domain in the plane, with nonstandard boundary conditions (BCs) of nonlocal type. They argue that similar convergence results and error estimates hold as those established for elliptic EVPs for a scalar function, with classical local BCs of Dirichlet, Neumann or Robin type. Here, the nonlocal character of the BCs constitutes a major difficulty in the analysis, requiring the introduction and error estimation of a new, suitably modified (vector) Lagrange interpolant on the finite element mesh. The theoretical error estimate for the eigenvalue is confirmed by an illustrative numerical example.
reviewed by: Ziwen Jiang
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1423315
zbMATH Keywords: finite element methods
zbMATH Keywords: vector-valued functions
zbMATH Keywords: second-order elliptic eigenvalue problems
zbMATH Keywords: nonstandard boundary conditions
zbMATH Keywords: convergence
zbMATH Keywords: error estimation
zbMATH Keywords: numerical example
author: H. De Schepper
author: Roger Van Keer
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00122-3
OpenAlex ID: W2011286392
description: scientific article; zbMATH DE number 1423315