Topical Problems of Fluid Mechanics


Institute of Thermomechanics AS CR, v.v.i.	CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics	MIO Université du Sud Toulon Var - AMU - CNRS - IRD	Czech Pilot centre ERCOFTAC

Stability of Finite Element - Finite Volume Discretizations of Convection -Diffusion - Reaction Equations
Deuring P., Eymard E.
Abstract:
We consider a time-dependent and a steady linear convection-diffusion-reaction equation. These equations are approximately solved by a combinedfinite element - finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a tri- angular grid, and the convection and reaction term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is used as time discretization. This scheme is unconditionally L2-stable, uniformly with respect to the diffusion coeffcient
Keywords:
convection-diffusion-reaction equation, combined finite element - finite volume method, Crouzeix-Raviart finite elements, barycentric finite volumes, upwind method, stability.

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In Proceedings Topical Problems of Fluid Mechanics 2015, Prague, 2015 Edited by David Šimurda and Tomáš Bodnár, pp. 47-52 ISBN 978-80-87012-55-0 (Print) ISSN 2336-5781 (Print)