Equal-order interpolations: A unified approach to stabilize the incompressible and advective effects. (English) Zbl 0898.76068

We present a SUPG formulation for compressible and near incompressible Navier-Stokes equations. It introduces an extension of the exact solution for one-dimensional systems to the multidimensional case, in a similar way to that arising in the scalar problem. This formulation satisfies both the one-dimensional advective-diffusive system limit case and the advection-dominated multidimensional system case. Another feature of this formulation is that it introduces naturally a stabilizing term for the incompressibility condition. However, in our formulation the stabilization is introduced to the whole system of equations, while other authors introduce a term to stabilize the incompressibility condition and another one for the advective term.


76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76D05 Navier-Stokes equations for incompressible viscous fluids
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