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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {40},
year = {2006},
pages = {785-814},
doi = {10.1051/m2an:2006030},
mrnumber = {2274778},
zbl = {1133.76332},
language = {en},
url = {http://dml.mathdoc.fr/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 40 (2006) pp. 785-814. doi : 10.1051/m2an:2006030. http://gdmltest.u-ga.fr/item/M2AN_2006__40_4_785_0/
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