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A relationship between stabilized finite element methods and the Galerkin method with bubble functions. (English) Zbl 0756.76044
Summary: A relation between stabilized finite element methods and the Galerkin method employing interpolations with bubble functions is established for the advective-diffusive model and for the linearized compressible Navier- Stokes equations. The bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy. In particular, for the advective-diffusive model, the Galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline-upwind/Petrov-Galerkin method in the diffusive limit.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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