Figueroa, Leonardo and Suli, Endre (2011) Greedy approximation of highdimensional OrnsteinUhlenbeck operators with unbounded drift. Technical Report. Foundations of Computational Mathematics. (Submitted)
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Abstract
We investigate the convergence of a nonlinear approximation method introduced by Ammar et al. (cf. J. NonNewtonian Fluid Mech. 139:153176, 2006) for the numerical solution of highdimensional FokkerPlanck equations featuring in NavierStokesFokkerPlanck systems that arise in kinetic models of dilute polymers. In the case of Poisson's equation on a rectangular domain in , subject to a homogeneous Dirichlet boundary condition, the mathematical analysis of the algorithm was carried out recently by Le Bris, Lelievre and Maday (Const. Approx. 30: 621651, 2009), by exploiting its connection to greedy algorithms from nonlinear approximation theory explored, for example, by DeVore and Temlyakov (Adv. Comput. Math. 5:173187, 1996); hence, the variational version of the algorithm, based on the minimization of a sequence of Dirichlet energies, was shown to converge. In this paper, we extend the convergence analysis of the pure greedy and orthogonal greedy algorithms considered by Le Bris, Lelievre and Maday to the technically more complicated case where the Laplace operator is replaced by a highdimensional OrnsteinUhlenbeck operator with unbounded drift, of the kind that appears in FokkerPlanck equations that arise in beadspring chain type kinetic polymer models with finitely extensible nonlinear elastic potentials, posed on a highdimensional Cartesian product configuration space D = D_1 x ... x D_N contained in , where each set D_i, i=1,...,N, is a bounded open ball in , d = 2, 3.
Item Type:  Technical Report (Technical Report) 

Subjects:  A  C > Approximations and expansions H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1058 
Deposited By:  Lotti Ekert 
Deposited On:  17 Apr 2011 07:12 
Last Modified:  29 May 2015 18:44 
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Greedy approximation of highdimensional OrnsteinUhlenbeck operators with unbounded drift. (deposited 05 Mar 2011 13:41)
 Greedy approximation of highdimensional OrnsteinUhlenbeck operators with unbounded drift. (deposited 17 Apr 2011 07:12) [Currently Displayed]
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