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

Authors:
G. Matthies;L. Tobiska
Affiliations:
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
Venue:
International Journal of Computing Science and Mathematics
Year:
2007

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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.