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

Abstract

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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.

How to cite

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Bonito, 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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