A finite element method for elliptic eigenvalue problems in a multi-component domain in 2D with nonlocal Dirichlet transition conditions
The authors consider linear elliptic eigenvalue problems of second-order on bounded domains which are composed of a number of convex polygonal subdomains. On the outer boundaries classical mixed Robinson-Dirichlet boundary conditions are given, while on the interfaces between two subdomains nonlocal Dirichlet transition conditions are imposed. The problem is written in variational form and finite element approximations are studied. An asymptotic error analysis is presented which rests upon properties of an imperfect Lagrange interpolant and on a cruxial density result. Attention is also paid to computational aspects. For a model problem numerical results are presented.
scientific article; zbMATH DE number 1398834