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The Crank–Nicolson finite spectral element method and numerical simulations for 2D non‐stationary Navier–Stokes equations
Author(s) -
Luo Zhendong,
Jiang Wenrui
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6039
Subject(s) - mathematics , discretization , crank–nicolson method , quadrilateral , navier–stokes equations , finite element method , bilinear interpolation , mathematical analysis , convergence (economics) , spectral element method , stability (learning theory) , extended finite element method , statistics , physics , economic growth , compressibility , economics , thermodynamics , machine learning , computer science , engineering , aerospace engineering
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.