Finite element method for viscoelastic fluids flows: approximation of the Maxwell model

We discuss about the finite element approximation of viscoelastic fluid flow. We consider a fluid obeying the Oldroyd model and particularly we study the purely viscoelastic case, the so-called Maxwell model, important in practice for the applications. We examine two kinds of methods used for the approximation of the Maxwell model: method using a splitting technique and finite element method satisfying inf-sup conditions relating tensor and velocity. We present numerical results for these methods and we discuss about their stability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)