Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients

Abstract

We propose and analyze a $C^0$ spectral element method for a model eigenvalue problem with discontinuous coefficients in the one dimensional setting. A super-geometric rate of convergence is proved for the piecewise constant coefficients case and verified by numerical tests. Furthermore, the asymptotical equivalence between a Gauss-Lobatto collocation method and a spectral Galerkin method is established for a simplified model.