Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control

作     者：Mejdi Azaiez Kevin Le Balc'h 

作者机构：Universite de BordeauxBordeaux-INPI2M UMR5295F-33400TalenceFrance InriaSorbonne UniversiteUniversite de ParisCNRSLaboratoire Jacques-Louis LionsParisFrance 

出 版 物：《Annals of Applied Mathematics》 (应用数学年刊（英文版）)

年 卷 期：2024年第40卷第2期

页      面：191-218页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the French National Research Agency ANR-22-CE46-0005(NumOpTES) supported by the grant"Numerical simulation and optimal control in view of temperature regulation in smart buildings"of the Nouvelle Aquitaine Region partially supported by the Project TRECOS ANR-20-CE40-0009 funded by the ANR(2021-2024) 

主　　题：Boussinesq system penalty method stabilization feedback control 

摘      要：We investigate the numerical approximation for stabilizing the semidiscrete linearized Boussinesq system around an unstable stationary *** is attained through internal feedback controls applied to the velocity and temperature equations,localized within an arbitrary open *** study follows the framework presented in[14],considering the continuous linearized Boussinesq *** primary objective is to explore the penalizationbased approximation of the free divergence condition in the semidiscrete case and provide a numerical validation of these results in a two-dimensional setting.