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Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift

David J. KnezevicEndre Süli — 2009

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is concerned with the analysis and implementation of spectral Galerkin methods 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 U that is equal to + along the boundary D of the computational domain D . Using a symmetrization...

Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift

David J. KnezevicEndre Süli — 2008

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the analysis and implementation of spectral Galerkin methods 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 that is equal to +∞ along the boundary ∂ of the computational domain . Using a symmetrization...

A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model

David J. KnezevicEndre Süli — 2009

ESAIM: Mathematical Modelling and Numerical Analysis

We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computational point of view. The heterogeneous alternating-direction scheme combines a spectral Galerkin method for...

A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation

Dinh Bao Phuong HuynhDavid J. KnezevicAnthony T. Patera — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric . The method is based on static condensation at the interdomain level, a conforming eigenfunction “port” representation...

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