On an external finite element method for a second-order eigenvalue problem on a concave 2D-domain with Dirichlet boundary conditions

摘要

This paper deals with a finite element method for a second-order elliptic eigenvalue problem on a concave two-dimensional domain with Dirichlet boundary conditions. In the method a variational crime is committed in that the approximate eigenvalue problem is formulated on a domain Ωh which is not included in the original domain. Hence, the finite element approximation space Vh used is not a subspace of the Sobolev space entering the continuous variational problem. We obtain an optimal error estimate from above for the approximate eigenvalues under weaker conditions for the data than in other papers. Moreover, a basic result for the error of the elliptic projection is proved in a different manner.