Continuous Data Assimilation for the Double-Diffusive Natural Convection

In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in space. The long time stability and convergence results are presented for different options of nudging parameters. Two elaborative numerical test are given in order to confirm the theory and prove the promise of the algorithm.