A Certified Reduced Basis Method for the Fokker–Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow

DOI10.1137/090759239zbMath1226.82051OpenAlexW2003207029MaRDI QIDQ3084404

Anthony T. Patera, David J. Knezevic

Publication date: 16 March 2011

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/090759239

zbMATH Keywords

micro-macro modelFokker-Planck equationgreedy algorithma posteriori error estimationreduced basis methodsproper orthogonal decomposition (POD)polymeric fluidsfinitely extensible nonlinear elastic (FENE) dumbbells

Mathematics Subject Classification ID

Non-Newtonian fluids (76A05) Initial-boundary value problems for second-order parabolic equations (35K20) Statistical mechanics of polymers (82D60) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fokker-Planck equations (35Q84)

Related Items (14)

CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS ⋮ A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations ⋮ Reduced basis techniques for stochastic problems ⋮ Error estimate of the non-intrusive reduced basis (NIRB) two-grid method with parabolic equations ⋮ Certified reduced basis model validation: a frequentistic uncertainty framework ⋮ A POD-EIM reduced two-scale model for crystal growth ⋮ A two-step certified reduced basis method ⋮ Certified reduced basis methods for parametrized parabolic partial differential equations with non-affine source terms ⋮ A natural-norm successive constraint method for inf-sup lower bounds ⋮ An hp Certified Reduced Basis Method for Parametrized Parabolic Partial Differential Equations ⋮ Reduced basis approximation anda posteriorierror estimates for a multiscale liquid crystal model ⋮ Model order reduction and error estimation with an application to the parameter-dependent eddy current equation ⋮ REDUCED BASIS APPROXIMATION ANDA POSTERIORIERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS ⋮ A POD–EIM reduced two-scale model for precipitation in porous media

Uses Software

• SLEPc
• PETSc

This page was built for publication: A Certified Reduced Basis Method for the Fokker–Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow