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Pré-Publication, Document De Travail Année : 2024

Analysis and Discontinuous Galerkin approximation of the Boussinesq system with Navier-type boundary condition

Résumé

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.
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Dates et versions

hal-04096856 , version 1 (13-05-2023)
hal-04096856 , version 2 (09-04-2024)

Identifiants

  • HAL Id : hal-04096856 , version 2

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Afaf Bouharguane, Nour Seloula. Analysis and Discontinuous Galerkin approximation of the Boussinesq system with Navier-type boundary condition. 2024. ⟨hal-04096856v2⟩
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