The Discrete Duality Finite Volume method for the Stokes equations on 3-D polyhedral meshes

Stella Krell (1, 2) , Gianmarco Manzini (3)

1 COFFEE - COmplex Flows For Energy and Environment
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 IMATI-CNR - Istituto di Matematica Applicata e Tecnologie Informatiche

We develop a Discrete Duality Finite Volume (\DDFV{}) method for the three-dimensional steady Stokes problem with a variable viscosity coefficient on polyhedral meshes. Under very general assumptions on the mesh, which may admit non-convex and non-conforming polyhedrons, we prove the stability and well-posedness of the scheme. We also prove the convergence of the numerical approximation to the velocity, velocity gradient and pressure, and derive a priori estimates for the corresponding approximation error. Final numerical experiments confirm the theoretical predictions.

Mots clés: 3-D Stokes equations; discrete duality finite volume method; polyhedral mesh; variable viscosity

Domaines: Equations aux dérivées partielles [math.AP]

Stella Krell, Gianmarco Manzini. The Discrete Duality Finite Volume method for the Stokes equations on 3-D polyhedral meshes. SIAM Journal on Numerical Analysis, 2012, 50 (2), pp.808-837. ⟨10.1137/110831593⟩. ⟨hal-00448465v2⟩