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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 ( h  3/4 ) for the finite element/finite volume method. These error estimates are compared and confirmed by the numerical experiments.

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