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A High Accuracy Spectral Element Method for Solving Eigenvalue Problems

A triangular spectral element method is proposed and analyzed for the Laplacian Eigen value problem. The method is based on the Galerkin approximation with generalized Koornwinder polynomials. We detailedly describe the approximation scheme and implementation for solving the Laplacian Eigen value problem. Numerical experiments also indicate that the triangular spectral element method for solving the Eigen value problems on convex domain has the "spectral" accuracy, that is, exponential convergence rate.