Title: Mass conservation of finite element methods for coupled flow-transport problems

Authors: G. Matthies, L. Tobiska

Addresses: Fakultat fur Mathematik, Ruhr-Universitat Bochum, Universitatsstrasse 150, 44780 Bochum, Germany. ' Institut fur Analysis und Numerik, Otto-von-Guericke-Universitat Magdeburg, Postfach 4120, 39016 Magdeburg, Germany

Abstract: This paper gives an overview of the mass conservation properties of finite element discretisations applied to coupled flow-transport problems. The system is described by the instationary, incompressible Navier–Stokes equations and the time-dependent transport equation. Due to the incompressibility constraint, the weak solution of the transport equation satisfies a global mass conservation. Since the discretised velocity fulfils only a discrete incompressibility constraint, the global mass conservation is, in general, satisfied only approximately. Several discretisations which ensure the global mass conservation, also on the discrete level, will be studied.

Keywords: Navier–Stokes equations; transport equation; global mass conservation; flow transport; finite element discretisation; FEM; finite element method; incompressibility.

DOI: 10.1504/IJCSM.2007.016537

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.293 - 307

Published online: 07 Jan 2008 *

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