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| Numerical Study of Semidiscrete PenaltyApproach for Stabilizing BoussinesqSystem with Localized Feedback Control |
| Mejdi Azaiez,K′evin Le Balc’h |
| (Universit′e de Bordeaux, Bordeaux-INP, I2M UMR5295, F-33400,Talence, France;Inria, Sorbonne Universit′e, Universit′e de Paris, CNRS, Laboratoire Jacques-Louis Lions, Paris, France) |
| DOI： |
| 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 penalizationbased approximation of the free divergence condition in the semidiscrete case
and provide a numerical validation of these results in a two-dimensional setting |
| Key words: Boussinesq system, penalty method, stabilization, feedback control. |