Chebyshev-Legendre Spectral Method for Solving the Two-dimensional Vorticity Equations with Homogeneous Dirichlet Conditions

摘要

The Chebyshev-Legendre spectral method for the two-dimensional vorticity equations is considered. The Legendre Galerkin Chebyshev collocation method is used with the Chebyshev-Gauss collocation points. The numerical analysis results under the L-2-norm for the Chebyshev-Legendre method of one-dimensional case are generalized into that of the two-dimensional case. The stability and optimal order convergence of the method are proved. Numerical results are given.