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Existence of approximate solutions and error bounds for viscoelastic fluid flow: Characteristics method. (English) Zbl 0923.76098
Summary: In this paper we study a finite element approximation of a steady viscoelastic fluid flow obeying an Oldroyd B type constitutive law. The approximate stress, velocity, and pressure are, respectively, \(P_1\) discontinuous, \(P_2\) continuous, \(P_1\) continuous. We use the method of characteristics for the convection of the extra stress tensor. We suppose that the continuous problem admits a sufficiently smooth and sufficiently small solution. We show by a fixed point method that the approximate problem has a solution and an error bound is given.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76A10 Viscoelastic fluids
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