Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes

Stella Krell (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

''Discrete Duality Finite Volume'' schemes (DDFV for short) on general meshes are studied here for Stokes problems with variable viscosity with Dirichlet boundary conditions. The aim of this work is to analyze the well-posedness of the scheme and its convergence properties. The DDFV method requires a staggered scheme, the discrete unknowns, the components of the velocity and the pressure, are located on different nodes. The scheme is stabilized using a finite volume analogue to Brezzi-Pitkäranta techniques. This scheme is proved to be well-posed on general meshes and to be first order convergent in a discrete $H^1$-norm and a discrete $L^2$-norm for respectively the velocity and the pressure. Finally numerical experiments confirm the theoretical prediction, in particular on locally refined non conformal meshes.

Domaines: Equations aux dérivées partielles [math.AP]

Stella Krell. Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes. Numerical Methods for Partial Differential Equations, 2011, 27 (6), pp.1666-1706. ⟨10.1002/num.20603⟩. ⟨hal-00385687v2⟩