UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS  

作　　者：Shipeng Mao Jiaao Sun Wendong Xue 

机构地区：[1]NCMIS,LSEC,Institute of Computational Mathematics and Scientific/Enginnering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Journal of Computational Mathematics》2024年第1期71-110,共40页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11871467,11471329).

摘　　要：In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关 键 词：Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence 

分 类 号：O24[理学—计算数学]