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.
['Gunar Matthies', 'Lutz Tobiska']
Mass conservation of finite element methods for coupled flow-transport problems