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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.

MSC:

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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