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.


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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