| Issue |
ESAIM: M2AN
Volume 35, Number 5, September-October 2001
|
|
|---|---|---|
| Page(s) | 879 - 897 | |
| DOI | https://doi.org/10.1051/m2an:2001140 | |
| Published online | 15 April 2002 | |
Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows
Département de Mathématiques,
École Polytechnique Fédérale de Lausanne,
1015 Lausanne, Switzerland.
Received:
17
January
2001
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.
Mathematics Subject Classification: 65N30 / 65N12 / 76A10
Key words: Viscoelastic fluids / Galerkin Least Square finite elements.
© EDP Sciences, SMAI, 2001
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