Abstract
This paper concerns the mixed Laguerre–Legendre spectral approximation and its application to numerical simulation of incompressible flow in an infinite strip. Some approximation results in weighted Sobolev spaces are given. A Laguerre–Legendre spectral scheme for the stream function form of Navier–Stokes equations is constructed. The stability and the convergence of the proposed scheme are proved. The numerical experiments show the high accuracy of this method. The main techniques used in this paper are also applicable to other nonlinear partial differential equations in an infinite strip.
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