Remarks on discretizations of convection terms in Hybrid mimetic mixed methods

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

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

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.
Citation: Jérôme Droniou. Remarks on discretizations of convection terms in Hybrid mimetic mixed methods[J]. Networks and Heterogeneous Media, 2010, 5(3): 545-563. doi: 10.3934/nhm.2010.5.545

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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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