Resumen de Hydrodynamical modelling and multidimensional approximation of estuarian river flows

David Trujillo, Mohamed Amara

• We propose here a new approach for deriving 2D and 1D hydrodynamical models, within the framework of mixed variational formulations. We thus obtain a 2D-horizontal model, as well as a 2D-vertical and a 1D model taking into account the geometry of the river. We analyze here only the 3D model and the 2D-horizontal one, for which we propose (after time discretization) low-order conforming finite element approximations. All the variational problems are well-posed. We intend to justify next a posteriori estimators between these models.