A BUBBLE ELEMENT FOR THE COMPRESSIBLE EULER EQUATIONS

In this paper, we present a new Galerkin finite element method with bu bble function for the compressible Euler equations. This method is der ived from the scaled bubble element for the advection-diffusion proble ms developed by Simo and his colleagues, which is based on the equival ence between the Galerkin method employing piecewise linear interpolat ion with bubble functions and the Streamline-Upwind/Petrov Galerkin (S UPG) finite element method using P-1 approximation in the steady advec tion-diffusion problem. Simo and this author have applied this approac h to transient advection-diffusion problems by using a special scaled bubble function called P-scaled bubble, which is designed to work in t he transient advection-diffusion problems for any Peclet number from 0 to infinity. The method presented in this paper is an application of this P-scaled bubble element to a pure hyperbolic system.