稳态 $p(\cdot)$-Navier-Stokes 方程的有限元逼近误差分析
Error analysis for a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations
AI总结：
本文研究了稳态 $p(\cdot)$-Navier-Stokes 方程的有限元逼近，在自然分数阶正则性假设下证明了收敛阶，处理了对流项并采用更实用的幂律指数离散化，数值实验证实了速度先验误差估计的拟最优性。
摘要：
本文研究了稳态 $p(\cdot)$-Navier-Stokes 方程（$p(\cdot)$ 依赖于变量）的有限元逼近，并在假设速度矢量场和运动压力满足自然分数阶正则性假设下证明了收敛阶。与以往结果相比，本文处理了对流项，并对幂律指数 $p(\cdot)$ 采用了更实用的离散化方法。数值实验证实了先验误差估计（针对速度）在速度矢量场和运动压力的分数阶正则性假设下的拟最优性。
英文摘要：
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 $\textit{a priori}$ error estimates (for the velocity) with respect to fractional regularity assumptions on the velocity vector field and the kinematic pressure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
