Geodesic
Finite element analysis of a simplified stochastic hookean dumbbells model arising from viscoelastic flows
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 4, pp. 785-814

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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.

DOI : 10.1051/m2an:2006030
Classification : 46T, 65M, 76A
Keywords: viscoelastic, hookean dumbbells, finite elements, stochastic differential equations 
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     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 },
     pages = {785--814},
     publisher = {EDP-Sciences},
     volume = {40},
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     year = {2006},
     doi = {10.1051/m2an:2006030},
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     zbl = {1133.76332},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2006030/}
}
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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 , Tome 40 (2006) no. 4, pp. 785-814. doi: 10.1051/m2an:2006030

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