A RELATIONSHIP BETWEEN STABILIZED FINITE-ELEMENT METHODS AND THE GALERKIN METHOD WITH BUBBLE FUNCTIONS

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 (SUPG) method in the diffusive limit.