In this chapter we examine mass-conservation properties of finite element discretizations of coupled flow-transport problems. The system under consideration is described by the unsteady incompressible Navier-Stokes equations and a time-dependent transport equation; see [GS00a, GS00b, Hir88, Hir90] for models where this combination arises. The incompressibility constraint implies that global mass is conserved in the weak solution of the transport equation. Since the discretized velocity only satisfies a discrete incompressibility constraint, global mass is in general conserved only approximately in the numerical scheme. We shall investigate conditions under which discrete global mass conservation can be guaranteed.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Mass Conservation for Coupled Flow-Transport Problems. In: Robust Numerical Methods for Singularly Perturbed Differential Equations. Springer Series in Computational Mathematics, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34467-4_17
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DOI: https://doi.org/10.1007/978-3-540-34467-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34466-7
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