This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Giesselmann, JanPryer, Tristan2016-03-242019-06-2820130946-8633https://doi.org/10.34657/2317https://oa.tib.eu/renate/handle/123456789/3181We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of AllenCahn/CahnHilliard/NavierStokesKorteweg type which allows for phase transitions.We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.application/pdfeng510Quasi-incompressibilityAllen–CahnCahn–HilliardNavier–Stokes–Kortewegphase transitionenergy consistent/mimeticdiscontinuous Galerkin finite element methodZweiphasenströmungGalerkin-MethodeNumerisches ModellReport