# Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows

Marco Picasso; Jacques Rappaz^{[1]}

- [1] Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland

- Volume: 35, Issue: 5, page 879-897
- ISSN: 0764-583X

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topPicasso, Marco, and 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 35.5 (2001): 879-897. <http://eudml.org/doc/194078>.

@article{Picasso2001,

abstract = {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.},

affiliation = {Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland},

author = {Picasso, Marco, Rappaz, Jacques},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {viscoelastic fluids; Galerkin least square finite elements; simplified Oldroyd-B model; convex polygon; existence of solution; small relaxation times; continuous piecewise linear finite elements; Galerkin least square method; a priori error estimates; Newton-chord fixed point theorem; a posteriori error estimates; elastic viscous split stress scheme},

language = {eng},

number = {5},

pages = {879-897},

publisher = {EDP-Sciences},

title = {Existence, a priori and a posteriori error estimates for a nonlinear three-field problem arising from Oldroyd-B viscoelastic flows},

url = {http://eudml.org/doc/194078},

volume = {35},

year = {2001},

}

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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 5

SP - 879

EP - 897

AB - 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.

LA - eng

KW - viscoelastic fluids; Galerkin least square finite elements; simplified Oldroyd-B model; convex polygon; existence of solution; small relaxation times; continuous piecewise linear finite elements; Galerkin least square method; a priori error estimates; Newton-chord fixed point theorem; a posteriori error estimates; elastic viscous split stress scheme

UR - http://eudml.org/doc/194078

ER -

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