Viscoelastic Fluid Supg-cbb Finite Element Method

This paper gives a stabilized finite element method for viscoelastic fluid flow based on SUPG method and CBB method. The approximate stress.velocity and pressure are respectively Pk continuous, Pk+1 and Pk.The SUPG method is used for convection of the extra stress tensor ;the CBB (circumventing BB condition ) is used for the combination of the velocity and pressure spaces. When assuming the continuous problem admits a sufficiently smooth and sufficiently small solution,the approximate problem is proved to have a unique solution .and an error bound is given.