In this paper, we examine a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations ($p(\cdot)$ is variable dependent) and prove orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Compared to previous results, we treat the convective term and employ a more practicable discretization of the power-law index $p(\cdot)$. Numerical experiments confirm the quasi-optimality of the a priori error estimates (for the velocity) with respect to fractional regularity assumptions on the velocity vector field and the kinematic pressure.

翻译：本文研究稳态$p(\cdot)$-Navier-Stokes方程（其中$p(\cdot)$为可变参数）的有限元近似，在速度向量场和运动压力满足自然分数阶正则性假设的条件下，证明了收敛阶。与以往结果相比，我们对对流项进行了处理，并对幂律指数$p(\cdot)$采用了更实用的离散化方法。数值实验验证了先验误差估计（针对速度）关于速度向量场和运动压力分数阶正则性假设的拟最优性。