Abstract
The author studies a finite element approximation of viscoelastic fluid flow obeying an Oldroyd B type constitutive law. The approximate stress, velocity, and pressure are, respectively, $P_1 $ continuous, $P_2 $ continuous, and $P_1 $ continuous. The streamline upwinding Petrov–Galerkin method for the convection of the extra stress tensor is used. Suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution. It is shown by a fixed point method that the approximate problem has a solution and an error bound is given.
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