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Networks and Heterogeneous Media

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

  • 1.
    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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  • 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.


  • This article has been cited by:

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    3. Markus Bambach, Armin Fügenschuh, Johannes Buhl, Felix Jensch, Johannes Schmidt, Mathematical Modeling and Optimization for Powder-Based Additive Manufacturing, 2020, 47, 23519789, 1159, 10.1016/j.promfg.2020.04.158
    4. Donatella Granata, Luca Lorenzi, An Evaluation of Propagation of the HIV-Infected Cells via Optimization Problem, 2022, 10, 2227-7390, 2021, 10.3390/math10122021
    5. Fabian Gnegel, Armin Fügenschuh, Michael Hagel, Sven Leyffer, Marcus Stiemer, A solution framework for linear PDE-constrained mixed-integer problems, 2021, 188, 0025-5610, 695, 10.1007/s10107-021-01626-1
    6. Jesse Beisegel, Johannes Buhl, Rameez Israr, Johannes Schmidt, Markus Bambach, Armin Fügenschuh, 2023, Chapter 5, 978-981-99-0775-5, 121, 10.1007/978-981-99-0776-2_5
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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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