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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00448465
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Submitted on : Tuesday, June 14, 2011 - 3:17:52 PM
Last modification on : Monday, October 12, 2020 - 2:28:04 PM
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Stella Krell, Gianmarco Manzini. The Discrete Duality Finite Volume method for the Stokes equations on 3-D polyhedral meshes. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2012, 50 (2), pp.808-837. ⟨10.1137/110831593⟩. ⟨hal-00448465v2⟩

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