He Guoliang, Zhang Yong
School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 610056, China.
School of Medical Information and Engineering, Southwest Medical University, Luzhou 646099, China.
Entropy (Basel). 2022 May 30;24(6):768. doi: 10.3390/e24060768.
This paper proves the optimal estimations of a low-order spatial-temporal fully discrete method for the non-stationary Navier-Stokes Problem. In this paper, the semi-implicit scheme based on Euler method is adopted for time discretization, while the special finite volume scheme is adopted for space discretization. Specifically, the spatial discretization adopts the traditional triangle P1-P0 trial function pair, combined with macro element form to ensure local stability. The theoretical analysis results show that under certain conditions, the full discretization proposed here has the characteristics of local stability, and we can indeed obtain the optimal theoretic and numerical order error estimation of velocity and pressure. This helps to enrich the corresponding theoretical results.
本文证明了非定常纳维-斯托克斯问题的低阶时空全离散方法的最优估计。本文采用基于欧拉方法的半隐式格式进行时间离散，同时采用特殊的有限体积格式进行空间离散。具体而言，空间离散采用传统的三角形P1-P0试验函数对，并结合宏单元形式以确保局部稳定性。理论分析结果表明，在一定条件下，本文提出的全离散格式具有局部稳定性的特点，并且我们确实可以得到速度和压力的最优理论和数值阶误差估计。这有助于丰富相应的理论结果。
