Hybridization of mixed high-order methods on general meshes and application to the Stokes equations

Joubine Aghili 1, * Sébastien Boyaval 2, 3 Daniele Antonio Di Pietro 1
* Corresponding author
3 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : In this work we study the hybridization of the Mixed High-Order methods for diffusion problems recently introduced in [Di Pietro and Ern, "A family of arbitrary order mixed methods for heterogeneous anisotropic diffusion on general meshes", preprint hal-00918482]. As for classical mixed finite element methods, hybridization proceeds in two steps: first, the continuity of flux unknowns at interfaces is enforced via Lagrange multipliers and, second, flux variables are locally eliminated. As a result, we identify a primal coercive problem which is equivalent to the original mixed problem, and whose numerical solution is less expensive. New error estimates are derived, and the resulting primal hybrid method for diffusion is used as a basis to design an arbitrary-order method for the Stokes problem on general meshes. Implementation aspects are thoroughly discussed, and numerical validation is provided.
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https://hal.archives-ouvertes.fr/hal-01009723
Contributor : Daniele Antonio Di Pietro <>
Submitted on : Wednesday, June 18, 2014 - 3:09:41 PM
Last modification on : Wednesday, January 30, 2019 - 3:16:03 PM
Long-term archiving on : Thursday, September 18, 2014 - 11:11:24 AM

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  • HAL Id : hal-01009723, version 1

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Joubine Aghili, Sébastien Boyaval, Daniele Antonio Di Pietro. Hybridization of mixed high-order methods on general meshes and application to the Stokes equations. 2014. ⟨hal-01009723v1⟩

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