Previous |  Up |  Next


Title: Finite element approximation of a contact vector eigenvalue problem (English)
Author: de Schepper, Hennie
Author: van Keer, Roger
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 48
Issue: 6
Year: 2003
Pages: 559-571
Summary lang: English
Category: math
Summary: We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem. The error analysis involved is shown to be affected by the nonlocal condition, which requires a suitable modification of the vector Lagrange interpolant on the overall finite element mesh. Nevertheless, we arrive at optimal error estimates. In the last section, an illustrative numerical example is given, which confirms the theoretical results. (English)
Keyword: eigenvalue problem
Keyword: nonlocal coupling condition
Keyword: finite elements
MSC: 65N25
MSC: 65N30
idZBL: Zbl 1099.65106
idMR: MR2025964
DOI: 10.1023/B:APOM.0000024494.71246.d3
Date available: 2009-09-22T18:16:03Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] F. A.  Mehmeti, S.  Nicaise: Nonlinear interaction problems.Nonlinear Anal. 20 (1993), 27–61. MR 1199063, 10.1016/0362-546X(93)90183-S
Reference: [2] P. A.  Raviart, J. M. Thomas: Introduction à l’analyse numérique des équations aux dérivées partielles (2ième tirage).Masson, Paris, 1993.
Reference: [3] P. G.  Ciarlet: The Finite Element Method for Elliptic Problems.North Holland Publishing Company, Amsterdam, 1978. Zbl 0383.65058, MR 0520174
Reference: [4] M.  Vanmaele, R. Van Keer: An operator method for a numerical quadrature finite element approximation for a class of second-order elliptic eigenvalue problems in composite structures.RAIRO Model. Math. Anal. Numer. 29 (1995), 339–365. MR 1342711, 10.1051/m2an/1995290303391


Files Size Format View
AplMat_48-2003-6_14.pdf 356.2Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo