an:05074707
Zbl 1099.65106
De Schepper, Hennie; Van Keer, Roger
Finite element approximation of a contact vector eigenvalue problem
EN
Appl. Math., Praha 48, No. 6, 559-571 (2003).
00187964
2003
j
65N30
nonlocal coupling condition; finite elements
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.