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, Volume 40 (2006) no. 4, p. 785-814
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.
DOI : https://doi.org/10.1051/m2an:2006030
Classification:  46T,  65M,  76A
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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {4},
     year = {2006},
     pages = {785-814},
     doi = {10.1051/m2an:2006030},
     zbl = {1133.76332},
     mrnumber = {2274778},
     language = {en},
     url = {http://www.numdam.org/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, Volume 40 (2006) no. 4, pp. 785-814. doi : 10.1051/m2an:2006030. http://www.numdam.org/item/M2AN_2006__40_4_785_0/

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