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

Authors:
Andrea Bonito;Philippe Clément;Marco Picasso
Affiliations:
Ecole Polytechnique Fédérale de Lausanne, Institut d’Analyse et Calcul Scientifique, 1015, Lausanne, Switzerland;Leiden University, Mathematical Institute, P.O. Box 9512, NL-2300 RA, Leiden, The Netherlands;Ecole Polytechnique Fédérale de Lausanne, Institut d’Analyse et Calcul Scientifique, 1015, Lausanne, Switzerland
Venue:
Numerische Mathematik
Year:
2007

Citing 0
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Abstract

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.