Super-Geometric Convergence of Spectral Element Method for Eigenvalue Problems with Jump Coefficients (Journal of Computational Mathematics, 2018)
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.
Keywords: Eigenvalue; Spectral method; Collocation; Galerkin finite element method.