The Chebyshev spectral element approximation with exact quadratures

A new Chebyshev spectral element method has been developed in this paper, in which exact quadratures are used to overcome a shortfall of the Gauss–Chebyshev quadrature in variational spectral element projections. The method is validated with the Stokes and the Cauchy–Riemann problems. It is shown that an enhancement of the approximation convergence rate is attained, and numerical accuracy is much better than that from the Gauss–Lobatto–Legendre spectral element method.