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

Stella Krell (1) , Gianmarco Manzini (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 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. 2010. ⟨hal-00448465v1⟩