Resumen
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 streamline upwind Petrov--Galerkin (SUPG) approximation for the constitutive equation. We analyze both the semidiscrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error estimates for, the numerical approximations.