Free Access
Volume 43, Number 6, November-December 2009
Page(s) 1117 - 1156
Published online 01 August 2009
  1. A. Ammar, B. Mokdad, F. Chinesta and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J. Non-Newtonian Fluid Mech. 139 (2006) 153–176. [CrossRef]
  2. A. Ammar, B. Mokdad, F. Chinesta and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. Part II: Transient simulation using space-time separated representations. J. Non-Newtonian Fluid Mech. 144 (2007) 98–121. [CrossRef]
  3. S. Balay, K. Buschelman, V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith and H. Zhang, PETSc users manual. Tech. Rep. ANL-95/11 – Revision 2.1.5, Argonne National Laboratory (2004).
  4. J.W. Barrett and E. Süli, Existence of global weak solutions to dumbbell models for dilute polymers with microscopic cut-off. Math. Models Methods Appl. Sci. 18 (2008) 935–971. [CrossRef] [MathSciNet] [PubMed]
  5. B. Bialecki and R. Fernandes, An orthogonal spline collocation alternating direction implicit Crank-Nicolson method for linear parabolic problems on rectangles. SIAM J. Numer. Anal. 36 (1999) 1414–1434. [CrossRef] [MathSciNet]
  6. P.B. Bochev, M.D. Gunzburger and J.N. Shadid, Stability of the SUPG finite element method for transient advection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2301–2323. [CrossRef] [MathSciNet]
  7. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Second Edn., Springer (2002).
  8. M. Celia and G. Pinder, An analysis of alternating-direction methods for parabolic equations. Numer. Methods Part. Differ. Equ. 1 (1985) 57–70. [CrossRef]
  9. M. Celia and G. Pinder, Generalized alternating-direction collocation methods for parabolic equations. I. Spatially varying coefficients. Numer. Methods Partial Differ. Equ. 3 (1990) 193–214. [CrossRef]
  10. C. Chauvière and A. Lozinski, Simulation of complex viscoelastic flows using Fokker–Planck equation: 3D FENE model. J. Non-Newtonian Fluid Mech. 122 (2004) 201–214. [CrossRef]
  11. C. Chauvière and A. Lozinski, Simulation of dilute polymer solutions using a Fokker–Planck equation. Comput. Fluids 33 (2004) 687–696. [CrossRef]
  12. P. Clément, Approximation by finite element functions using local regularization. Rev. Française Automat. Informat. Recherche Opérationnelle Sér. RAIRO Anal. Numér. 9 (1975) 77–84.
  13. P. Delaunay, A. Lozinski and R.G. Owens, Sparse tensor-product Fokker–Planck-based methods for nonlinear bead-spring chain models of dilute polymer solutions. CRM Proc. Lect. Notes 41 (2007) 73–89.
  14. J. Douglas and T. Dupont, Alternating-direction Galerkin methods on rectangles. Numer. Solution Partial Differ. Equ. II (SYNSPADE 1970) (1971) 133–214.
  15. H. Eisen, W. Heinrichs and K. Witsch, Spectral collocation methods and polar coordinate singularities. J. Comput. Phys. 96 (1991) 241–257. [CrossRef] [MathSciNet]
  16. H. Elman, D. Silvester and A. Wathen, Finite elements and fast iterative solvers. Oxford Science Publications, UK (2005).
  17. C. Helzel and F. Otto, Multiscale simulations of suspensions of rod-like molecules. J. Comp. Phys. 216 (2006) 52–75. [CrossRef]
  18. W. Huang and B. Guo, Fully discrete Jacobi-spherical harmonic spectral method for Navier-Stokes equations. Appl. Math. Mech. 29 (2008) 453–476 (English Ed.). [CrossRef] [MathSciNet]
  19. B. Jourdain, T. Lelièvre and C. Le Bris, Existence of solution for a micro-macro model of polymeric fluid: the FENE model. J. Funct. Anal. 209 (2004) 162–193. [CrossRef] [MathSciNet]
  20. B.S. Kirk, J.W. Peterson, R.M. Stogner and G.F. Carey, libMesh: A C++ library for parallel adaptive mesh refinement/coarsening simulations. Eng. Comput. 23 (2006) 237–254. [CrossRef]
  21. D.J. Knezevic, Analysis and implementation of numerical methods for simulating dilute polymeric fluids. Ph.D. Thesis, University of Oxford, UK (2008),
  22. D.J. Knezevic and E. Süli, Spectral Galerkin approximation of Fokker–Planck equations with unbounded drift. ESAIM: M2AN 43 (2009) 445–485. [CrossRef] [EDP Sciences]
  23. A.N. Kolmogorov, Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Math. Ann. 104 (1931).
  24. T. Li and P. Zhang, Mathematical analysis of multi-scale models of complex fluids. Commun. Math. Sci. 5 (2007) 1–51. [MathSciNet]
  25. C. Liu and H. Liu, Boundary conditions for the microscopic FENE models. SIAM J. Appl. Math. 68 (2008) 1304–1315. [CrossRef] [MathSciNet]
  26. A. Lozinski, Spectral methods for kinetic theory models of viscoelastic fluids. Ph.D. Thesis, École Polytechnique Fédérale de Lausanne, Suisse (2003).
  27. A. Lozinski and C. Chauvière, A fast solver for Fokker–Planck equation applied to viscoelastic flows calculation: 2D FENE model. J. Computat. Phys. 189 (2003) 607–625. [CrossRef] [MathSciNet]
  28. J.N. Lyness and D. Jespersen, Moderate degree symmetric quadrature rules for the triangle. J. Inst. Math. Appl. 15 (1975) 19–32. [CrossRef] [MathSciNet]
  29. T. Matsushima and P.S. Marcus, A spectral method for polar coordinates. J. Comput. Phys. 120 (1995) 365–374. [CrossRef] [MathSciNet]
  30. H.C. Öttinger, Stochastic Processes in Polymeric Fluids. Springer (1996).
  31. R.G. Owens and T.N. Phillips, Computational Rheology. Imperial College Press (2002).
  32. C. Schwab, E. Süli and R.A. Todor, Sparse finite element approximation of high-dimensional transport-dominated diffusion problems. ESAIM: M2AN 42 (2008) 777–820. [CrossRef] [EDP Sciences]
  33. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [CrossRef] [MathSciNet] [PubMed]
  34. W.T.M. Verkley, A spectral model for two-dimensional incompressible fluid flow in a circular basin. I. Mathematical formulation. J. Comput. Phys. 136 (1997) 100–114. [CrossRef] [MathSciNet]
  35. N.J. Walkington, Quadrature on simplices of arbitrary dimension. nw0z/publications/00-CNA-023/023abs/.
  36. H.R. Warner, Kinetic theory and rheology of dilute suspensions of finitely extendible dumbbells. Ind. Eng. Chem. Fundamentals 11 (1972) 379–387. [CrossRef]
  37. H. Zhang and P. Zhang, Local existence for the FENE-dumbbell model of polymeric fluids. Arch. Ration. Mech. Anal. 181 (2006) 373–400. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you