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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2020038
Keywords: Stabilized finite element methods, viscoelastic fluids, Oldroyd-B, logarithm reformulation, high Weissenberg number problem
@article{M2AN_2021__55_S1_S279_0,
author = {Codina, Ramon and Moreno, Laura},
title = {Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {S279--S300},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {Suppl\'ement},
doi = {10.1051/m2an/2020038},
mrnumber = {4221325},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020038/}
}
TY - JOUR AU - Codina, Ramon AU - Moreno, Laura TI - Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - S279 EP - S300 VL - 55 IS - Supplément PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020038/ DO - 10.1051/m2an/2020038 LA - en ID - M2AN_2021__55_S1_S279_0 ER -
%0 Journal Article %A Codina, Ramon %A Moreno, Laura %T Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P S279-S300 %V 55 %N Supplément %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020038/ %R 10.1051/m2an/2020038 %G en %F M2AN_2021__55_S1_S279_0
Codina, Ramon; Moreno, Laura. Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S279-S300. doi: 10.1051/m2an/2020038
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