Regularity estimations of the 2D/3D unsteady incompressible Darcy-Brinkman equations with double-diffusive convection and their finite element analysis based on incremental pressure correction method

作     者：Jiang, Linlin Liu, Demin 

作者机构：Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Peoples R China 

出 版 物：《COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION》 (Comm. Nonlinear Sci. Numer. Simul.)

年 卷 期：2025年第143卷

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 0801[工学-力学（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：National Natural Science Foundation of China Research Fund from the Key Laboratory of Xinjiang Province [2022D04014] 

主　　题：Darcy-Brinkman equations Double-diffusive convection Regularity estimations Incremental pressure correction method Stability and convergence 

摘      要：In this paper, the 2D/3D unsteady incompressible Darcy-Brinkman equations with double- diffusive convection are considered. Firstly, several a priori regularity estimates of the weak solutions are derived, and then two fully decoupled incremental pressure correction finite element methods (IPC FEMs) are proposed, i.e., the first-order and second-order standard IPC (SIPC) methods. Based on the above regularity results, the unconditional stability and optimal error estimates for the first-order SIPC method are proved, and then the unconditional stability for the second-order SIPC method is established. Some numerical experiments are carried out to illustrate the effectiveness of the proposed methods.