Abstract
The Petrov-Galerkin finite element approximation employing the trilinear element with a bubble function is presented in this paper, which is equivalent to the stabilized finite element method in case of P1 approximation in certain problems such as steady advection-diffusion and viscous fluid flows. As an approximated function of the weighting funciton, the trilinear interpolation function with a special bubble function called stabilized bubble is used. The stabilized bubble element is establised using the stabilized bubble function with a control parameter. The shape of the bubble function as the weighting function can be changed to attain optimal numerical viscousity. The rotating cone, the standing vortex and the driven cavity problems are performed for the numerical examples.
