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)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LHSV - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics
3 MATHERIALS - MATHematics for MatERIALS

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.

Mots clés: diffusion; Stokes; general meshes; mixed high-order methods; hybridization

Domaines: Analyse numérique [math.NA]

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⟩