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

A Hybrid High-Order Method for the Steady Incompressible Navier–Stokes Problem 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 $$L^2$$ L 2 -norm of the pressure under a standard data smallness assumption. More precisely, when polynomials of degree $$k\ge 0$$ k ≥ 0 at mesh elements and faces are used, both quantities are proved to converge as $$h^{k+1}$$ h k + 1 (with h denoting the meshsize). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0512-x
Publisher site
See Article on Publisher Site

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 $$L^2$$ L 2 -norm of the pressure under a standard data smallness assumption. More precisely, when polynomials of degree $$k\ge 0$$ k ≥ 0 at mesh elements and faces are used, both quantities are proved to converge as $$h^{k+1}$$ h k + 1 (with h denoting the meshsize).

Journal

Journal of Scientific ComputingSpringer Journals

Published: Aug 4, 2017

References

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