Geodesic
Finite element approximation of a contact vector eigenvalue problem
Applications of Mathematics, Tome 48 (2003) no. 6, pp. 559-571.

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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.
DOI : 10.1023/B:APOM.0000024494.71246.d3
Classification : 65N25, 65N30
Keywords: eigenvalue problem; nonlocal coupling condition; finite elements 
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de Schepper, Hennie; van Keer, Roger. Finite element approximation of a contact vector eigenvalue problem. Applications of Mathematics, Tome 48 (2003) no. 6, pp. 559-571. doi : 10.1023/B:APOM.0000024494.71246.d3. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024494.71246.d3/

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