The Discrete Duality Finite Volume Method for Stokes Equations on Three-Dimensional Polyhedral Meshes

Authors:
Stella Krell;Gianmarco Manzini
Affiliations:
krell@latp.univ-mrs.fr;Marco.Manzini@imati.cnr.it
Venue:
SIAM Journal on Numerical Analysis
Year:
2012

Citing 11
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Abstract

We develop a discrete duality finite volume 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 nonconforming 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.