Construction of stabilization operators for Galerkin least-squares discretizations of compressible and incompressible flows
The design and analysis of a class of stabilization operators suitable for spacetime Galerkin least-squares finite element discretizations of the symmetrized compressible NavierStokes 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, R.M.J. van Damme, Analysis of stabilization operators for Galerkin least-squares discretizations of the incompressible NavierStokes equations, Comput. Methods Appl. Mech. Engrg. 195 (2006) 9821006]. 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 NavierStokes equations satisfies the entropy condition, which ensures global nonlinear stability of the discretization.
stabilization operator compressible navierstokes equations incompressible limit galerkin least-squares finite element methods