Non-inf-sup-stable finite element approximations to the incompressible Navier–Stokes equations based on equal-order spaces for velocity and pressure are studied in this paper. To account for the violation of the discrete inf-sup condition, different types of symmetric pressure stabilization terms are considered. It is shown in the numerical analysis that these terms also improve stabilization of dominating convection in the following sense: error bounds with constants independent of inverse powers of the viscosity are derived. For proving the bound for the |$L^2$| error of the pressure the choice of a suitable initial approximation for the velocity is essential.

中文翻译：

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时间相关的Navier–Stokes方程的等阶有限元逼近的对称压力稳定

本文研究了基于速度和压力的等阶空间的不可压缩的Navier–Stokes方程的非insups稳定稳态有限元逼近。为了解决对离散注入条件的违反，考虑了不同类型的对称压力稳定项。在数值分析中显示，这些术语还从以下意义上改善了对流的稳定性：得出了具有与粘度的反幂无关的常数的误差范围。用于证明| $ L ^ 2 $ |的边界 压力误差选择合适的速度初始近似值至关重要。