an:01658294
Zbl 0988.65100
De Schepper, Hennie
Finite element analysis of a coupling eigenvalue problem on overlapping domains
EN
J. Comput. Appl. Math. 132, No. 1, 141-153 (2001).
00077045
2001
j
65N25 65N15 65N30 35P15
eigenvalue problem; nonlocal coupling condition; finite elements; elliptic eigenvalue problem; error analysis
A nonstandard elliptic eigenvalue problem on a rectangular domain, consisting of two overlapping rectangles, where the interaction is expressed through an integral coupling condition is considered. Finite element (FE) discretizations with and without numerical quadrature are derived The error analysis is affected by the nonlocal coupling condition, which requires the introduction and error estimation of a suitably modified Lagrange interpolant on the FE mesh. As a consequence, the resulting error estimates are suboptimal compared to the ones for the classical eigenvalue problems.
Wilhelm Heinrichs (Essen)