Low-order finite element method for the well-posed bidimensional Stokes problem

Michel Salaün (1) , Stéphanie Salmon (2)

1 ICA - Institut Clément Ader
2 LMR - Laboratoire de Mathématiques de Reims

We work on a low-order finite element approximation of the vorticity, velocity and pressure formulation of the bidimensional Stokes problem. In a previous paper, we have introduced the adequate space in which to look for the vorticity in order to have a well-posed problem. In this paper, we deal with the numerical approximation of this space, prove optimal convergence of the scheme and show numerical experiments in good accordance with the theory. We remark that despite one supplementary unknown(the vorticity), results of the scheme are much better than the ones obtained with the P1 plus bubble−P1 element in the velocity–pressure formulation.

Mots clés: Stokes problem; Vorticity–velocity–pressure formulation; Mixed formulation; Finite elements method; Harmonic functions; Integral method

Domaines: Analyse numérique [cs.NA]

Michel Salaün, Stéphanie Salmon. Low-order finite element method for the well-posed bidimensional Stokes problem. IMA Journal of Numerical Analysis, 2015, 35 (1), pp.427-453. ⟨10.1093/imanum/drt063⟩. ⟨hal-01939301⟩