# 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 (2010)

- 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 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 -

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