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

Marco Picasso; Jacques Rappaz

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

Abstract

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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.

How to cite

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Picasso, 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 35.5 (2010): 879-897. <http://eudml.org/doc/197557>.

@article{Picasso2010,
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. },
author = {Picasso, Marco, Rappaz, Jacques},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Viscoelastic fluids; Galerkin Least Square finite elements.; viscoelastic fluids; 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},
month = {3},
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/197557},
volume = {35},
year = {2010},
}

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
DA - 2010/3//
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.; viscoelastic fluids; 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/197557
ER -

References

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