Least squares h-p spectral element method for elliptic eigenvalue problems

In this paper we discuss how to solve elliptic eigenvalue problems on polygonal domains using least squares methods. Exponential rate of convergence has been obtained for approximate eigenvalues as well as the eigenfunctions. The result is proved when the boundary of underlying domain is smooth and also when the boundary contains corners. The computational results confirm the error estimates. The results proved in the paper are valid for multiple or clustered eigenvalues also. The method works for non-self adjoint problems too.