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Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations

✍ Scribed by A. Montlaur; S. Fernandez-Mendez; J. Peraire; A. Huerta

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
254 KB
Volume
64
Category
Article
ISSN
0271-2091

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✦ Synopsis

Abstract

An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high‐order piecewise divergence‐free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.

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## Abstract We develop the energy norm __a posteriori__ error analysis of exactly divergence‐free discontinuous RT~__k__~/__Q__~__k__~ Galerkin methods for the incompressible Navier–Stokes equations with small data. We derive upper and local lower bounds for the velocity–pressure error measured in