A least squares approach for exponential rate of convergence of eigenfunctions of second order elliptic eigenvalue problem

DOI: 10.5176/2251-1911_CMCGS14.32

Authors: Lokendra K. Balyan

Abstract: In this paper, we show that the convergence estimates for eigenvalues and eigenvectors of second order elliptic eigenvalues 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 are to be assumed sufficiently smooth and the coefficients of the differential operator are analytic.

Keywords: approximation of eigenvalues and eigenvectors; compact operator; non-conforming; spectral element method; elliptic operators; smooth boundary