# Finite-element discretizations of a two-dimensional grade-two fluid model

Vivette Girault; Larkin Ridgway Scott

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 35, Issue: 6, page 1007-1053
- ISSN: 0764-583X

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topGirault, Vivette, and Scott, Larkin Ridgway. "Finite-element discretizations of a two-dimensional grade-two fluid model." ESAIM: Mathematical Modelling and Numerical Analysis 35.6 (2010): 1007-1053. <http://eudml.org/doc/197420>.

@article{Girault2010,

abstract = {
We propose and analyze several finite-element schemes for solving a grade-two
fluid model, with a
tangential boundary condition, in a two-dimensional polygon. The exact
problem is split into a
generalized Stokes problem and a transport equation, in such a way that it
always has a solution
without restriction on the shape of the domain and on the size of the data.
The first scheme uses
divergence-free discrete velocities and a centered discretization of the
transport term, whereas the
other schemes use Hood-Taylor discretizations for the velocity and
pressure, and either a centered or an upwind
discretization of the transport term. One facet of our analysis is
that, without restrictions on the data,
each scheme has a discrete solution and all discrete solutions converge
strongly to solutions of the
exact problem. Furthermore, if the domain is convex and the data satisfy
certain conditions, each
scheme satisfies error inequalities that lead to error estimates.
},

author = {Girault, Vivette, Scott, Larkin Ridgway},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Mixed formulation; divergence-zero
finite elements; inf-sup condition; uniform W1,p-stability;
Hood-Taylor method; streamline diffusion.; mixed formulation; tangential boundary condition; two-dimensional polygon; generalized-Stokes problem; -stability; streamline diffusion; transport equation; divergence-free discrete velocities; centered discretization; Hood-Taylor discretizations; error estimates},

language = {eng},

month = {3},

number = {6},

pages = {1007-1053},

publisher = {EDP Sciences},

title = {Finite-element discretizations of a two-dimensional grade-two fluid model},

url = {http://eudml.org/doc/197420},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Girault, Vivette

AU - Scott, Larkin Ridgway

TI - Finite-element discretizations of a two-dimensional grade-two fluid model

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 6

SP - 1007

EP - 1053

AB -
We propose and analyze several finite-element schemes for solving a grade-two
fluid model, with a
tangential boundary condition, in a two-dimensional polygon. The exact
problem is split into a
generalized Stokes problem and a transport equation, in such a way that it
always has a solution
without restriction on the shape of the domain and on the size of the data.
The first scheme uses
divergence-free discrete velocities and a centered discretization of the
transport term, whereas the
other schemes use Hood-Taylor discretizations for the velocity and
pressure, and either a centered or an upwind
discretization of the transport term. One facet of our analysis is
that, without restrictions on the data,
each scheme has a discrete solution and all discrete solutions converge
strongly to solutions of the
exact problem. Furthermore, if the domain is convex and the data satisfy
certain conditions, each
scheme satisfies error inequalities that lead to error estimates.

LA - eng

KW - Mixed formulation; divergence-zero
finite elements; inf-sup condition; uniform W1,p-stability;
Hood-Taylor method; streamline diffusion.; mixed formulation; tangential boundary condition; two-dimensional polygon; generalized-Stokes problem; -stability; streamline diffusion; transport equation; divergence-free discrete velocities; centered discretization; Hood-Taylor discretizations; error estimates

UR - http://eudml.org/doc/197420

ER -

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