Numerical analysis of the DDFV method for the Stokes problem with mixed Neumann/Dirichlet boundary conditions

Thierry Goudon (1, 2) , Stella Krell (1, 3, 2, 4) , Giulia Lissoni (1, 3, 2)

1 COFFEE - COmplex Flows For Energy and Environment
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
4 UniCA - Université Côte d'Azur

The aim of this work is to analyze " Discrete Duality Finite Volume " schemes (DDFV for short) on general meshes by adapting the theory known for the linear Stokes problem with Dirichlet boundary conditions to the case of Neu-mann boundary conditions on a fraction of the boundary. We prove well-posedness for stabilized schemes and we derive some error estimates. Finally, we illustrate some numerical results in which we compare stabilized and unstabilized schemes.

Mots clés: Stokes system; DDFV scheme; Neumann boundary conditions

Domaines: Analyse numérique [math.NA]

Thierry Goudon, Stella Krell, Giulia Lissoni. Numerical analysis of the DDFV method for the Stokes problem with mixed Neumann/Dirichlet boundary conditions. FVCA8 - International Conference on Finite Volumes for Complex Applications VIII, Jun 2017, Lille, France. ⟨hal-01502397⟩