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.
Keywords: viscoelastic, hookean dumbbells, finite elements, stochastic differential equations
@article{M2AN_2006__40_4_785_0,
author = {Bonito, Andrea and Cl\'ement, Philippe and Picasso, Marco},
title = {Finite element analysis of a simplified stochastic hookean dumbbells model arising from viscoelastic flows},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {785--814},
year = {2006},
publisher = {EDP Sciences},
volume = {40},
number = {4},
doi = {10.1051/m2an:2006030},
mrnumber = {2274778},
zbl = {1133.76332},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2006030/}
}
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: Modélisation mathématique et analyse numérique PY - 2006 SP - 785 EP - 814 VL - 40 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2006030/ DO - 10.1051/m2an:2006030 LA - en ID - M2AN_2006__40_4_785_0 ER -
%0 Journal Article %A Bonito, Andrea %A Clément, Philippe %A Picasso, Marco %T Finite element analysis of a simplified stochastic hookean dumbbells model arising from viscoelastic flows %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 785-814 %V 40 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2006030/ %R 10.1051/m2an:2006030 %G en %F M2AN_2006__40_4_785_0
Bonito, Andrea; Clément, Philippe; Picasso, Marco. Finite element analysis of a simplified stochastic hookean dumbbells model arising from viscoelastic flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 4, pp. 785-814. doi: 10.1051/m2an:2006030
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