SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1660-1686, August 2024.
Abstract. 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.

中文翻译：

---

具有非齐次狄利克雷边界条件的稳态广义纳维-斯托克斯方程的有限元离散


《SIAM 数值分析杂志》，第 62 卷，第 4 期，第 1660-1686 页，2024 年 8 月。

抽象的。我们提出了对具有剪切相关粘度的流体的稳定广义纳维-斯托克斯方程进行有限元离散化，并使用非均匀狄利克雷边界条件和非均匀发散约束完成。我们建立了离散解的（弱）收敛性以及速度矢量场和标量运动压力的先验误差估计。数值实验补充了理论发现。