Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S279 - S300|
|Published online||26 February 2021|
Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem
Universitat Politècnica de Catalunya, Jordi Girona 1-3, Edifici C1, Barcelona 08034, Spain
2 CIMNE – Centre Internacional de Mètodes Numèrics en Enginyeria, Gran Capità S/N, Barcelona 08034, Spain
* Corresponding author: firstname.lastname@example.org
Accepted: 26 May 2020
In this paper we present the numerical analysis of a finite element method for a linearized viscoelastic flow problem. In particular, we analyze a linearization of the logarithmic reformulation of the problem, which in particular should be able to produce results for Weissenberg numbers higher than the standard one. In order to be able to use the same interpolation for all the unknowns (velocity, pressure and logarithm of the conformation tensor), we employ a stabilized finite element formulation based on the Variational Multi-Scale concept. The study of the linearized problem already serves to show why the logarithmic reformulation performs better than the standard one for high Weissenberg numbers; this is reflected in the stability and error estimates that we provide in this paper.
Mathematics Subject Classification: 65N12 / 76A10 / 76M10
Key words: Stabilized finite element methods / viscoelastic fluids / Oldroyd-B / logarithm reformulation / high Weissenberg number problem
© EDP Sciences, SMAI 2021
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