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September  2010, 5(3): 545-563. doi: 10.3934/nhm.2010.5.545

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, France

Received  January 2010 Revised  April 2010 Published  July 2010

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.
Keywords: convection-dominated problems, Hybrid Mixed Mimetic method, flow in porous media., elliptic-parabolic coupled problems, Mixed finite volume, Hybrid finite volume, convection-diffusion equation, Mimetic finite difference.
Mathematics Subject Classification: Primary: 65N12, 65N30, 65M12, 65M6.
Citation: Jérôme Droniou. Remarks on discretizations of convection terms in Hybrid mimetic mixed methods. Networks and Heterogeneous Media, 2010, 5 (3) : 545-563. doi: 10.3934/nhm.2010.5.545
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