Quadrature finite element method for elliptic eigenvalue problems

Abstract

A positive semi-definite eigenvalue problem for second-order self-adjoint elliptic differential operator definedon a bounded domain in the planewith smooth boundary and Dirichlet boundary condition is considered. This problem has a nondecreasing sequence of positive eigenvalues of finite multiplicity with a limit point at infinity. To the sequence of eigenvalues, there corresponds an orthonormal system of eigenfunctions. The original differential eigenvalue problem is approximated by the finite element method with numerical integration and Lagrange curved triangular finite elements of arbitrary order. Error estimates for approximate eigenvalues and eigenfunctions are established.