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 - <p style="text-align: justify;">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.</p>