Approximation of Time-Dependent Viscoelastic Fluid Flow: SUPG Approximation

In this article we consider the numerical approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG approximation for the constitutive equation. We analyse both the semi-discrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error estimates for, the numerical approximations.