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galerkin least square finite elements.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Existence, a priori and a posteriori error estimatesfor a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows
Marco Picasso, Jacques Rappaz
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 35 / Issue 5 / September 2001

Published online by Cambridge University Press:

15 April 2002, pp. 879-897

Print publication:

September 2001
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In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B modelwithout convective terms is considered. Assuming the domain to be a convexpolygon, existence of a solutionis proved for small relaxation times.Continuous piecewise linear finite elements together witha Galerkin Least Square (GLS) method are studied for solving this problem.Existence and a priori error estimatesare 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 methodis introduced. Numerical results confirm the theoretical predictions.