A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensions AstaggeredschemefortheStokesequations

Philippe Blanc (1) , Robert Eymard (2) , Raphaèle Herbin (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

This paper presents a new finite volume scheme for the steady Stokes equations on a general 2D mesh. The scheme is staggered, i.e. the discrete velocities are not located at the same place as the discrete pressures. We prove the existence and the uniqueness of a discrete solution. We then prove convergence of the discrete velocities to theweak solution of the problem. Under additional regularity conditions, we prove the convergence of a penalized version of the scheme to the weak solution of the problem. Numerical experiments on problems with known analytical solutions allow to obtain the rate of convergence for both velocities and pressure

Mots clés: Stokes equations; cell-centered finite volumes; unstructured mesh

Domaines: Analyse numérique [math.NA]

Philippe Blanc, Robert Eymard, Raphaèle Herbin. A staggered finite volume scheme on general meshes for the generalized Stokes problem in two space dimensions AstaggeredschemefortheStokesequations. International Journal on Finite Volumes, 2005, 2 (1), pp.1-31. ⟨hal-01112399⟩