Knezevic, David and Suli, Endre (2007) Spectral Galerkin approximation of FokkerPlanck equations with unbounded drift. Technical Report. Unspecified. (Submitted)

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Abstract
The paper is concerned with the analysis and implementation of a spectral Galerkin method for a class of FokkerPlanck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential U that is equal to +∞ along the boundary ∂D of the computational domain D. Using a symmetrization of the differential operator based on the Maxwellian M corresponding to U, which vanishes along ∂D, we remove the unbounded drift coefficient at the expense of introducing a degeneracy, through M, in the principal part of the operator. The class of admissible potentials includes the FENE (finitely extendible nonlinear elastic) model. We show the existence of weak solutions to the initialboundaryvalue problem, and develop a fully discrete spectral Galerkin approximation of such degenerate FokkerPlanck equations that exhibits optimalorder convergence in the Maxwellianweighted H1 norm on D. The theoretical results are illustrated by numerical experiments for the FENE model in two space dimensions.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1086 
Deposited By:  Lotti Ekert 
Deposited On:  07 May 2011 08:03 
Last Modified:  29 May 2015 18:46 
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