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Journal of Scientific Computing

, Volume 74, Issue 3, pp 1677–1705 | Cite as

A Hybrid High-Order Method for the Steady Incompressible Navier–Stokes Problem

  • Daniele A. Di Pietro
  • Stella KrellEmail author
Article

Abstract

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier–Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and is (relatively) inexpensive thanks to the possibility of statically condensing a subset of the unknowns at each nonlinear iteration. We show under general assumptions the existence of a discrete solution, which is also unique provided a data smallness condition is verified. Using a compactness argument, we prove convergence of the sequence of discrete solutions to minimal regularity exact solutions for general data. For more regular solutions, we prove optimal convergence rates for the energy-norm of the velocity and the \(L^2\)-norm of the pressure under a standard data smallness assumption. More precisely, when polynomials of degree \(k\ge 0\) at mesh elements and faces are used, both quantities are proved to converge as \(h^{k+1}\) (with h denoting the meshsize).

Keywords

Hybrid high-order Incompressible Navier–Stokes Polyhedral meshes Compactness Error estimates 

Mathematics Subject Classification

65N08 65N30 65N12 35Q30 76D05 

Notes

Acknowledgements

The work of D. A. Di Pietro was supported by Agence Nationale de la Recherche project HHOMM (ANR-15-CE40-0005).

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Institut Montpelliérain Alexander GrothendieckUniversité de MontpellierMontpellierFrance
  2. 2.Université Côte d’Azur, CNRS, Inria, LJADNiceFrance

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