具有初始数据的二维纳维-斯托克斯方程有限元方法的一致误差估计

Uniform Error Estimates of the Finite Element Method for the Navier-Stokes Equations in R2 with Initial Data.

作者信息

Ren Shuyan, Wang Kun, Feng Xinlong

机构信息

College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China.

出版信息

Entropy (Basel). 2023 Apr 27;25(5):726. doi: 10.3390/e25050726.

DOI:10.3390/e25050726

PMID:37238481

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10217603/

Abstract

In this paper, we study the finite element method of the Navier-Stokes equations with the initial data belonging to the L2 space for all time t>0. Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the H1-norm, when t∈[0,1). Under the uniqueness condition, by applying the integral technique and the estimates in the negative norm, we deduce the uniform-in-time optimal error bounds for the velocity in H1-norm and the pressure in L2-norm.

摘要

在本文中，我们研究了纳维 - 斯托克斯方程的有限元方法，其初始数据对于所有(t > 0)都属于(L^2)空间。由于初始数据的光滑性较差，尽管在(t\in[0,1))时，问题的解在(H^1)范数下是奇异的。在唯一性条件下，通过应用积分技术和负范数估计，我们推导出了速度在(H^1)范数和压力在(L^2)范数下与时间无关的最优误差界。