On the stability of colocated clustered finite volume simplicial discretizations for the 2D Stokes problem
Résumé
We study in this paper a novel cell-centered colocated finite volume scheme for the two-dimensional Stokes problem. Its definition involves two grids. The coarsest one is a triangulation of the computational domain in acute angles simplices; these triangles are called clusters. The control volumes grid is a finer one, built by cutting each cluster along the lines joining the mid-edge points to obtain four sub-triangles. By building explicitly a Fortin projection operator, we prove that the pair of discrete spaces associating the classical cell-centered approximation for the velocities and cluster-wide constant pressures is {\it inf-sup} stable. In a second step, we prove that a stabilization involving pressure jumps only across the internal edges of the clusters yields a stable scheme with the usual colocated discretization (\ie\ with the cell-centered approximation for the velocity and the pressure). We finally give an interpretation of this stabilization as a "minimal stabilization procedure", as introduced by Brezzi and Fortin.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)
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