Application of the least-squares spectral element method using Chebyshev polynomials to solve the incompressible Navier-Stokes equations

In this paper the extension of the Legendre least-squares spectral element formulation to Chebyshev polynomials will be explained. The new method will be applied to the incompressible Navier-Stokes equations and numerical results, obtained for the lid-driven cavity flow at Reynolds numbers varying between 1000 and 7500, will be compared with the commonly used benchmark results. The new results reveal that the least-squares spectral element formulations based on the Legendre and Chebyshev Gauss-Lobatto Lagrange interpolating polynomials are equally accurate.