This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, which includes three independent unknowns: the vorticity, velocity, and pressure. In dimension two, we establish an optimal error estimate for the three unknowns. The discretization is deduced from the implicit Euler scheme in time and spectral methods in space. We present a matrix linear system and some numerical tests, which are in perfect concordance with the analysis.

中文翻译：

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Navier-Stokes方程非平稳涡旋速度压力公式的解析和实现

本文讨论了迭代算法以及二维和三维中与时间相关的Navier–Stokes方程的光谱离散化的实现。我们提出了一个变分公式，其中包括三个独立的未知数：涡度，速度和压力。在第二维中，我们为三个未知数建立了最佳误差估计。从时间的隐式欧拉方案和空间的频谱方法推导离散。我们提出了矩阵线性系统和一些数值测试，这些分析与分析完全一致。