Remarks on discretizations of convection terms in Hybrid mimetic mixed methods

Jérôme Droniou

doi:10.3934/nhm.2010.5.545

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2010, Volume 5, Issue 3: 545-563. Doi: 10.3934/nhm.2010.5.545

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Remarks on discretizations of convection terms in Hybrid mimetic mixed methods

Jérôme Droniou^1,

1.
Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugène Bataillon, 34095 Montpellier cedex 5

Received: December 31, 2009

Revised: March 31, 2010

Published: August 2010

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Abstract

We present different ways, coming from Finite Volume or Mixed Finite Element frameworks, to discretize convection terms in Hybrid Finite Volume, Mimetic Finite Difference and Mixed Finite Volume methods for elliptic equations. We compare them through several numerical tests, deducing some generic principles, depending on the situation, on the choice of an apropriate method and its parameters. We also present an adaptation to the Navier-Stokes equations, with a numerical tests in the case of the lid-driven cavity.

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Mathematics Subject Classification: Primary: 65N12, 65N30, 65M12, 65M60.

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