Error analysis of finite element and finite volume methods for some viscoelastic fluids

We present the error analysis of a particular Oldroyd-B type model with the limiting Weissenberg number going to infinity. Assuming a suitable regularity of the exact solution we study the error estimates of a standard finite element method and of a combined finite element/finite volume method. Our theoretical result shows first order convergence of the finite element method and the error of the order O(h) for the finite element/finite volume method. These error estimates are compared and confirmed by the numerical experiments.