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Volume 40, Issue 2
Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control

Mejdi Azaiez & Kévin Le Balc’h

DOI: 10.4208/aam.OA-2024-0013

Ann. Appl. Math., 40 (2024), pp. 191-218.

Published online: 2024-05

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  • Abstract

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

  • Keywords

Boussinesq system, penalty method, stabilization, feedback control.

  • AMS Subject Headings

49N10, 93B05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-40-191, author = {Azaiez , Mejdi and Balc’h , Kévin Le}, title = {Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control}, journal = {Annals of Applied Mathematics}, year = {2024}, volume = {40}, number = {2}, pages = {191--218}, abstract = {

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

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2024-0013}, url = {http://global-sci.org/intro/article_detail/aam/23100.html} }
TY - JOUR T1 - Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control AU - Azaiez , Mejdi AU - Balc’h , Kévin Le JO - Annals of Applied Mathematics VL - 2 SP - 191 EP - 218 PY - 2024 DA - 2024/05 SN - 40 DO - http://doi.org/10.4208/aam.OA-2024-0013 UR - https://global-sci.org/intro/article_detail/aam/23100.html KW - Boussinesq system, penalty method, stabilization, feedback control. AB -

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

Azaiez , Mejdi and Balc’h , Kévin Le. (2024). Numerical Study of Semidiscrete Penalty Approach for Stabilizing Boussinesq System with Localized Feedback Control. Annals of Applied Mathematics. 40 (2). 191-218. doi:10.4208/aam.OA-2024-0013
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