Nowadays, coupled models are increasingly used in a wide variety of fields. For coupled problems, the use of separated data assimilation schemes in each medium is not satisfactory since the result of such assimilation process is generally inconsistent across the interface, thus leading to unacceptable artefacts. Hence, there is a strong need for adapting existing data assimilation techniques to the coupled framework. In this context, we propose three assimilation algorithms based on variational data assimilation techniques, which are applied to a simple coupled problem. The dynamical equations of this problem are coupled using an iterative Schwarz domain decomposition method. The aim is to properly take into account the coupling in the assimilation process in order to obtain a coupled solution close to the observations while satisfying the physical conditions across the interface. These algorithms are distinguished by their choice of cost function and control vector as well as their need to reach convergence of the iterative coupling method. Finally the performance of the methods are compared in terms of computational cost and accuracy. It showed promising results and the next objective is to apply such methods to ocean-atmosphere coupled models, by considering increasingly complex models including physical parametrisations for subgrid scales.