We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint. We establish (weak) convergence of discrete solutions as well as a priori error estimates for the velocity vector field and the scalar kinematic pressure. Numerical experiments complement the theoretical findings.

翻译：针对具有剪切依赖性粘度的流体，我们提出了一种适用于稳态、广义Navier-Stokes方程的有限元离散化方法，该方法同时处理非齐次Dirichlet边界条件和非齐次散度约束。本文建立了离散解的（弱）收敛性，并给出了速度向量场和标量运动压力的先验误差估计。数值实验对理论结果进行了补充验证。