Chebyshev-Legendre Spectral Domain Decomposition Method for Two-Dimensional Vorticity Equations (Communications in Computational Physics, 2020)
We extend the Chebyshev-Legendre spectral method to multi-domain casefor solving the two-dimensional vorticity equations. The schemes are formulated inLegendre-Galerkin method while the nonlinear term is collocated at Chebyshev-Gausscollocation points. We introduce proper basis functions in order that the matrix of algebraicsystem is sparse. The algorithm can be implemented efficiently and in parallelway. The numerical analysis results in the case of one-dimensional multi-domain aregeneralized to two-dimensional case. The stability and convergence of the method areproved. Numerical results are given.