On a finite element method for second order elliptic eigenvalue problems with nonlocal direchlet boundary conditions

Abstract

We consider a class of eigenvalue problems (EVPs) on a bounded convex polygonal domain Ω in the plane, with nonlocal Dirichlet boundary conditions (BCs) on Г⊂∂Ωand with local Robin or Dirich-let type BCs on ∂Ω\\Г. Choosing a proper space V as the space of trial- and testfunctions, we can recast the problem into the framework of abstract variational EVPs, as studied e.g. in [7]. Introducing suitable (families of) finite element subspaces V$sub:A$esub: of V, error estimates are established for the finite element approximations of the eigenpairs. The error analysis mainly rests upon the properties of a properly introduced imperfect Lagrange interpolant. The basic ideas are illustrated by means of a numerical example.