Energy consistent discontinuous Galerkin methods for the Navier–Stokes–Korteweg systemMakridakis, C., Giesselmann, J. and Pryer, T. (2014) Energy consistent discontinuous Galerkin methods for the Navier–Stokes–Korteweg system. Mathematics of Computation, 83 (289). pp. 2071-2099. ISSN 1088-6842 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1090/S0025-5718-2014-02792-0 Abstract/SummaryWe design consistent discontinuous Galerkin finite element schemes for the approximation of the Euler-Korteweg and the Navier-Stokes-Korteweg systems. We show that the scheme for the Euler-Korteweg system is energy and mass conservative and that the scheme for the Navier-Stokes-Korteweg system is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to viscous effects, that is, there is no numerical dissipation. In this sense the methods are consistent with the energy dissipation of the continuous PDE systems. - See more at: http://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02792-0/home.html#sthash.rwTIhNWi.dpuf
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