In this work, we handle a time-dependent Navier-Stokes problem in dimension three with a mixed boundary conditions. The variational formulation is written considering three independent unknowns: vorticity, velocity, and pressure. We use the backward Euler scheme for time discretization and the spectral method for space discretization. We present a complete numerical analysis linked to this variational formulation, which leads us to a priori error estimate.

中文翻译：

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具有混合边界条件的时间相关 Navier-Stokes 问题的谱离散化

在这项工作中，我们处理具有混合边界条件的三维时间相关的 Navier-Stokes 问题。编写变分公式时考虑了三个独立的未知数：涡度、速度和压力。我们使用后向欧拉方案进行时间离散化和谱法进行空间离散化。我们提出了与这个变分公式相关的完整数值分析，这导致我们先验误差估计。