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.