A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress exponents $p > \tfrac{2d}{d+2}$. The Dirichlet boundary condition is imposed strongly, using any discretization of the boundary data which converges at a sufficient rate. $\textit{A priori}$ error estimates for velocity vector field and kinematic pressure are derived and numerical experiments are conducted. These confirm the quasi-optimality of the $\textit{a priori}$ error estimate for the velocity vector field. The $\textit{a priori}$ error estimates for the kinematic pressure are quasi-optimal if $p \leq 2$.

翻译：本文提出了一种针对稳态、不可压缩、完全非齐次广义Navier-Stokes方程的有限元离散化方法。通过散度重构算子法，该公式适用于所有剪切应力指数 $p > \tfrac{2d}{d+2}$。Dirichlet边界条件采用强加方式，允许使用任何以足够收敛速率逼近边界数据的离散化方案。推导了速度矢量场与运动学压力的先验误差估计，并进行了数值实验。实验证实了速度矢量场先验误差估计的拟最优性。当 $p \leq 2$ 时，运动学压力的先验误差估计具有拟最优性。