A Least Squares Approach for Exponential Rate of Convergence of Eigenfunctions of Second-Order Elliptic Eigenvalue Problem

In this paper, we show the convergence estimates for eigenvalues and eigenvectors of second-order elliptic eigenvalue problems using spectral element method. A least squares approach is used to prove that the eigenvalues and eigenvectors converge exponentially in P, degree of polynomials, when the boundary of the domains is to be assumed sufficiently smooth and the coefficients of the differential operator are analytic.