Construction of stabilization operators for Galerkin least-squares discretizations of compressible and incompressible flows

M.A. Polner, L. Pesch, Jacobus J.W. van der Vegt

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    8 Citations (Scopus)

    Abstract

    The design and analysis of a class of stabilization operators suitable for space-time Galerkin least-squares finite element discretizations of the symmetrized compressible Navier-Stokes equations is discussed. The obtained stabilization matrix is well defined in the incompressible limit and reduces to the matrix described in [M. Polner, J.J.W. van der Vegt and R.M.J. van Damme, Analysis of stabilization operators for Galerkin least-squares discretizations of the incompressible Navier-Stokes equations, Comput. Meth. Appl. Mech. Eng., 195(2006):982--1006]. The stabilization matrix is investigated to give necessary and sufficient conditions for its positive definiteness. Under these conditions on the stabilization matrix, the Galerkin least-squares method for the symmetrized compressible Navier-Stokes equations satisfies the entropy condition, which ensures global nonlinear stability of the discretization.
    Original languageUndefined
    Article number10.1016/j.cma.2007.01.003
    Pages (from-to)2431-2448
    Number of pages18
    JournalComputer methods in applied mechanics and engineering
    Volume196
    Issue number1/21-24
    DOIs
    Publication statusPublished - 2007

    Keywords

    • EWI-8552
    • IR-63818
    • METIS-241934

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