Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, p. 879-897

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.

Classification:  65N30,  65N12,  76A10
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     pages = {879-897},
     zbl = {0997.76051},
     mrnumber = {1866272},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 35 (2001) no. 5, pp. 879-897. http://www.numdam.org/item/M2AN_2001__35_5_879_0/

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