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In this study, we analyzed a continuous data assimilation scheme applied on adouble-diffusive natural convection model. The algorithm is introduced with afirst order backward Euler time scheme along with a finite elementdiscretization in space. The long time stability and convergence results arepresented for different options of nudging parameters. Two elaborativenumerical test are given in order to confirm the theory and prove the promiseof the algorithm.

Continuous Data Assimilation for the Double-Diffusive Natural Convection