In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved for small relaxation times. Continuous piecewise linear finite elements together with a Galerkin Least Square (GLS) method are studied for solving this problem. Existence and a priori error estimates are established using a Newton-chord fixed point theorem, a posteriori error estimates are also derived. An Elastic Viscous Split Stress (EVSS) scheme related to the GLS method is introduced. Numerical results confirm the theoretical predictions.
Mots clés : viscoelastic fluids, Galerkin least square finite elements
@article{M2AN_2001__35_5_879_0,
author = {Picasso, Marco and Rappaz, Jacques},
title = {Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from {Oldroyd-B} viscoelastic flows},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {879--897},
publisher = {EDP-Sciences},
volume = {35},
number = {5},
year = {2001},
mrnumber = {1866272},
zbl = {0997.76051},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_5_879_0/}
}
TY - JOUR AU - Picasso, Marco AU - Rappaz, Jacques TI - Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 879 EP - 897 VL - 35 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_5_879_0/ LA - en ID - M2AN_2001__35_5_879_0 ER -
%0 Journal Article %A Picasso, Marco %A Rappaz, Jacques %T Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 879-897 %V 35 %N 5 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_5_879_0/ %G en %F M2AN_2001__35_5_879_0
Picasso, Marco; Rappaz, Jacques. Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 879-897. http://www.numdam.org/item/M2AN_2001__35_5_879_0/
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