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Energy consistent discontinuous Galerkin methods for the Navier–Stokes–Korteweg system

Makridakis, 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

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To link to this item DOI: 10.1090/S0025-5718-2014-02792-0


We 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:

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:40915
Publisher:American Mathematical Society

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