Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows
Picasso, Marco ; Rappaz, Jacques1
1 Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland
ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 5, pp. 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
Mots-clés : viscoelastic fluids, Galerkin least square finite elements
Picasso, Marco  ; Rappaz, Jacques 1

1 Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland 
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     title = {Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from {Oldroyd-B} viscoelastic flows},
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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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