@techreport{NA-07/16,
  abstract = "The paper is concerned with the analysis and implementation of a spectral Galerkin method for a class of Fokker-Planck 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&nbsp;<em>U</em>&nbsp;that is equal to +&infin; along the boundary &part;<em>D</em>&nbsp;of the computational domain&nbsp;<em>D</em>. Using a symmetrization of the differential operator based on the Maxwellian&nbsp;<em>M</em>corresponding to&nbsp;<em>U</em>, which vanishes along &part;<em>D</em>, we remove the unbounded drift coefficient at the expense of introducing a degeneracy, through&nbsp;<em>M</em>, 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 initial-boundary-value problem, and develop a fully discrete spectral Galerkin approximation of such degenerate Fokker-Planck equations that exhibits optimal-order convergence in the Maxwellian-weighted&nbsp;<strong>H</strong><sup>1</sup>&nbsp;norm on&nbsp;<em>D</em>. The theoretical results are illustrated by numerical experiments for the FENE model in two space dimensions.",
  author = "David J. Knezevic and Endre S\"{u}li",
  institution = "Oxford University Computing Laboratory",
  month = "September",
  number = "NA-07/16",
  title = "Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift",
  year = "2007",
}