The Crank–Nicolson finite spectral element method and numerical simulations for 2D non-stationary Navier–Stokes equations |
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| Authors: | Zhendong Luo Wenrui Jiang |
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| Institution: | 1. School of Mathematics and Physics, North China Electric Power University, Beijing, China;2. School of Control and Computer Engineering, North China Electric Power University, Beijing, China |
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| Abstract: | In this paper, we first build a semi-discretized Crank–Nicolson (CN) model about time for the two-dimensional (2D) non-stationary Navier–Stokes equations about vorticity–stream functions and discuss the existence, stability, and convergence of the time semi-discretized CN solutions. And then, we build a fully discretized finite spectral element CN (FSECN) model based on the bilinear trigonometric basic functions on quadrilateral elements for the 2D non-stationary Navier–Stokes equations about the vorticity–stream functions and discuss the existence, stability, and convergence of the FSECN solutions. Finally, we utilize two sets of numerical experiments to check out the correctness of theoretical consequences. |
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| Keywords: | existence and stability as well as convergence fully discretized finite spectral element Crank–Nicolson model semi-discretized Crank–Nicolson model two-dimensional non-stationary Navier–Stokes equations about vorticity-stream functions |
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