Remarks on discretizations of convection terms in Hybrid mimetic mixed methods

Pages: 545 - 563, Volume 5, Issue 3, September 2010

doi:10.3934/nhm.2010.5.545       Abstract        Full Text (5497.3K)       Related Articles

Jérôme Droniou - Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, CC 051, Place Eugène Bataillon, 34095 Montpellier cedex 5, France (email)

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.

Keywords:  Mixed finite volume, Hybrid finite volume, Mimetic finite difference, Hybrid Mixed Mimetic method, convection-diffusion equation, convection-dominated problems, elliptic-parabolic coupled problems, flow in porous media.
Mathematics Subject Classification:  Primary: 65N12, 65N30, 65M12, 65M60.

Received: January 2010;      Revised: April 2010;      Published: July 2010.