# Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows

Andrea Bonito; Philippe Clément; Marco Picasso

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

- Volume: 40, Issue: 4, page 785-814
- ISSN: 0764-583X

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topBonito, Andrea, Clément, Philippe, and Picasso, Marco. "Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows." ESAIM: Mathematical Modelling and Numerical Analysis 40.4 (2006): 785-814. <http://eudml.org/doc/249762>.

@article{Bonito2006,

abstract = {
A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded.
A finite element discretization in space is proposed.
Existence of the numerical solution is proved for small data, so as a priori error estimates,
using an implicit function theorem and regularity results obtained in [Bonito et al., J. Evol. Equ.6 (2006) 381–398] for the solution of the continuous problem. A posteriori error estimates are also derived.
Numerical results with small time steps and a large number of realizations confirm the
convergence rate with respect to the mesh size.
},

author = {Bonito, Andrea, Clément, Philippe, Picasso, Marco},

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

keywords = {Viscoelastic; Hookean dumbbells; finite elements; stochastic differential equations.; viscoelastic; stochastic differential equations},

language = {eng},

month = {11},

number = {4},

pages = {785-814},

publisher = {EDP Sciences},

title = {Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows},

url = {http://eudml.org/doc/249762},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Bonito, Andrea

AU - Clément, Philippe

AU - Picasso, Marco

TI - Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2006/11//

PB - EDP Sciences

VL - 40

IS - 4

SP - 785

EP - 814

AB -
A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded.
A finite element discretization in space is proposed.
Existence of the numerical solution is proved for small data, so as a priori error estimates,
using an implicit function theorem and regularity results obtained in [Bonito et al., J. Evol. Equ.6 (2006) 381–398] for the solution of the continuous problem. A posteriori error estimates are also derived.
Numerical results with small time steps and a large number of realizations confirm the
convergence rate with respect to the mesh size.

LA - eng

KW - Viscoelastic; Hookean dumbbells; finite elements; stochastic differential equations.; viscoelastic; stochastic differential equations

UR - http://eudml.org/doc/249762

ER -

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