A Class of Spectral Element Methods and Its A PrioriA Posteriori Error Estimates for 2nd-Order Elliptic Eigenvalue Problems

Abstract EN

This paper discusses spectral and spectral element methods with Legendre-Gauss-Lobatto nodal basis for general 2nd-order elliptic eigenvalue problems.

The special work of this paper is as follows.

(1) We prove a priori and a posteriori error estimates for spectral and spectral element methods.

(2) We compare between spectral methods, spectral element methods, finite element methods and their derived p-version, h-version, and hp-version methods from accuracy, degree of freedom, and stability and verify that spectral methods and spectral element methods are highly efficient computational methods.