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Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

Bonito, Andrea ; Clément, Philippe ; Picasso, Marco

In: Numerische Mathematik, 2007, vol. 107, no. 2, p. 213-255

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    Titre
    • Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow
    Auteur
    • Bonito, Andrea. Institut d'Analyse et Calcul Scientifique, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
    • Clément, Philippe. Mathematical Institute, Leiden University, P.O. Box 9512, NL-2300 RA, Leiden, The Netherlands
    • Picasso, Marco. Institut d'Analyse et Calcul Scientifique, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
    Type de document
    • Postprint
    Identifiant OAI-PMH
    • oai:doc.rero.ch:311096
    Summary
    A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem