A New Discontinuous Galerkin Formulation for the Boussinesq system with Navier-type boundary condition
BOUHARGUANE, Afaf
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
BOUHARGUANE, Afaf
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]
Langue
en
Document de travail - Pré-publication
Résumé en anglais
In this work we propose and analyze a discontinuous Galerkin method for the nonlinear coupled Navier-Stokes/temperature (or Boussinesq) equations with Navier-type boundary condition for the velocity. Existence and uniqueness ...Lire la suite >
In this work we propose and analyze a discontinuous Galerkin method for the nonlinear coupled Navier-Stokes/temperature (or Boussinesq) equations with Navier-type boundary condition for the velocity. Existence and uniqueness of the solution are obtained under a small data condition. We provide a priori error estimates in terms of a natural energy norms for the velocity, the pressure and the temperature. To our knowledge, it is the first time that a discontinuous Galerkin approximation for the full nonlinear coupled Bousinessq system, with Navier-type boundary condition for the velocity, is proposed and completely analyzed in both, continuous and discrete settings.< Réduire
Mots clés en anglais
discrete Sobolev inequality
Stationary Boussinesq equations
discontinuous Galerkin method
Navier boundary condition
fixed point theory
a priori error estimate
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