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

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Polner, M.A. and Pesch, L. and van der Vegt, J.J.W. (2007) Construction of stabilization operators for Galerkin least-squares discretizations of compressible and incompressible flows. Computer Methods in Applied Mechanics and Engineering, 196 (21-24). pp. 2431-2448. ISSN 0045-7825

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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.
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/63818
Official URL:http://dx.doi.org/10.1016/j.cma.2007.01.003
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