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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr


IMPACT FACTOR 2017: 0.658

CiteScore 2017: 1.05

SCImago Journal Rank (SJR) 2017: 1.291
Source Normalized Impact per Paper (SNIP) 2017: 0.893

Mathematical Citation Quotient (MCQ) 2017: 0.76

Online
ISSN
1609-9389
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Volume 15, Issue 2

Issues

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

Joubine Aghili / Sébastien Boyaval
  • Laboratoire d'hydraulique Saint-Venant (Ecole des Ponts ParisTech – EDF R&D – CEREMA), Université Paris Est and INRIA Rocquencourt (MATHERIALS), France
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/ Daniele A. Di Pietro
Published Online: 2015-03-03 | DOI: https://doi.org/10.1515/cmam-2015-0004

Abstract

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.

Keywords: Stokes; General Meshes; Mixed High-Order Methods; Hybridization

MSC: 65N30; 65N08

About the article

Received: 2014-10-22

Revised: 2015-02-06

Accepted: 2015-02-12

Published Online: 2015-03-03

Published in Print: 2015-04-01


Citation Information: Computational Methods in Applied Mathematics, Volume 15, Issue 2, Pages 111–134, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0004.

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Citing Articles

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Lorenzo Botti, Daniele A. Di Pietro, and Jérôme Droniou
Journal of Computational Physics, 2018
[2]
Lorenzo Botti, Daniele A. Di Pietro, and Jérôme Droniou
Computer Methods in Applied Mechanics and Engineering, 2018
[3]
Francesco Bonaldi, Daniele A. Di Pietro, Giuseppe Geymonat, and Françoise Krasucki
ESAIM: Mathematical Modelling and Numerical Analysis, 2018, Volume 52, Number 2, Page 393
[4]
Florent Chave, Daniele A. Di Pietro, and Luca Formaggia
SIAM Journal on Scientific Computing, 2018, Volume 40, Number 2, Page A1063
[5]
Joubine Aghili and Daniele A. Di Pietro
Journal of Scientific Computing, 2018
[6]
Daniele Boffi and Daniele A. Di Pietro
ESAIM: Mathematical Modelling and Numerical Analysis, 2018, Volume 52, Number 1, Page 1
[7]
M. Cicuttin, D.A. Di Pietro, and A. Ern
Journal of Computational and Applied Mathematics, 2017
[8]
Daniele A. Di Pietro and Stella Krell
Journal of Scientific Computing, 2017
[9]
Joubine Aghili, Daniele A. Di Pietro, and Berardo Ruffini
Computational Methods in Applied Mathematics, 2017, Volume 17, Number 3
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Daniele A. Di Pietro, Bernard Kapidani, Ruben Specogna, and Francesco Trevisan
IEEE Transactions on Magnetics, 2017, Volume 53, Number 6, Page 1
[11]
Daniele A. Di Pietro and Ruben Specogna
Journal of Computational Physics, 2016, Volume 326, Page 35
[12]
Daniele A. Di Pietro and Alexandre Ern
IMA Journal of Numerical Analysis, 2017, Volume 37, Number 1, Page 40
[13]
Daniele A. Di Pietro, Alexandre Ern, Alexander Linke, and Friedhelm Schieweck
Computer Methods in Applied Mechanics and Engineering, 2016, Volume 306, Page 175

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