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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2003

Vorticity-velocity-pressure and stream function-vorticity formulations for the Stokes problem

François Dubois
  • Fonction : Auteur
Michel Salaün

Résumé

For the Stokes problem in a two- or three-dimensional bounded domain with sufficiently smooth boundary, a new mixed formulation is presented by means of a vorticity-velocity-pressure formulation with a new Hilbert space for the vorticity. This new formulation allows arbitrary finite element meshes, especially tetrahedras, in standard numerical simulations based upon the marker-and-cell-method. The appropriate space for the vorticity is a space of square-integrable vector-valued functions with weak rotation that contains the usual space $H(curl, \Omega)$ of vector-valued functions, which, together with their curl, are square-integrable. The new mixed formulation is shown to be well-posed and provides the classical Stokes equations with a new boundary condition for tangential velocity on a subset of the boundary. However, it coincides with the classical boundary conditions for suitable domains such as in the two-dimensional case for a connected, open bounded domain.

Dates et versions

hal-00096367 , version 1 (19-09-2006)

Identifiants

Citer

François Dubois, Michel Salaün, Stéphanie Salmon. Vorticity-velocity-pressure and stream function-vorticity formulations for the Stokes problem. Journal de Mathématiques Pures et Appliquées, 2003, 82, num. 11, pp.1395-1451. ⟨10.1016/j.matpur.2003.09.002⟩. ⟨hal-00096367⟩
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