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Licensed Unlicensed Requires Authentication Published by De Gruyter March 3, 2015

Hybridization of Mixed High-Order Methods on General Meshes and Application to the Stokes Equations

  • Joubine Aghili EMAIL logo , Sébastien Boyaval and Daniele A. Di Pietro


This paper presents two novel contributions on the recently introduced Mixed High-Order (MHO) methods [`Arbitrary order mixed methods for heterogeneous anisotropic diffusion on general meshes', preprint (2013)]. We first address the hybridization of the MHO method for a scalar diffusion problem and obtain the corresponding primal formulation. Based on the hybridized MHO method, we then design a novel, arbitrary order method for the Stokes problem on general meshes. A full convergence analysis is carried out showing that, when independent polynomials of degree k are used as unknowns (at elements for the pressure and at faces for each velocity component), the energy-norm of the velocity and the L2-norm of the pressure converge with order (k + 1), while the L2-norm of the velocity (super-)converges with order (k + 2). The latter property is not shared by other methods based on a similar choice of unknowns. The theoretical results are numerically validated in two space dimensions on both standard and polygonal meshes.

MSC: 65N30; 65N08
Received: 2014-10-22
Revised: 2015-2-6
Accepted: 2015-2-12
Published Online: 2015-3-3
Published in Print: 2015-4-1

© 2015 by De Gruyter

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