Existence and equilibration of global weak solutions to kinetic models for dilute polymers II: Hookean-type models

Mathematical Models and Methods in Applied Sciences

Volumn 22, Issue 5, 2012, Pages

  Barrett, John W ^a   SÜli, Endre ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

compact embedding; Kinetic polymer models; NavierStokesFokkerPlanck system; Rouse chain; vector valued KolmogorovRiesz theorem; weighted Sobolev spaces

Indexed keywords

COMPACT EMBEDDING; NAVIERSTOKESFOKKERPLANCK SYSTEM; ROUSE CHAINS; VECTOR VALUED; WEIGHTED SOBOLEV SPACES;

DIFFUSION IN SOLIDS; DRAG; ENTROPY; FISHER INFORMATION MATRIX; KINETIC THEORY; KINETICS; PARTIAL DIFFERENTIAL EQUATIONS; SOBOLEV SPACES; TENSORS;

POLYMERS;

EID: 84857341975     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202511500242     Document Type: Review

References (18)

1. B. Andreianov, F. Boyer and F. Hubert, Discrete duality finite volume schemes for Leray-Lions type elliptic problems on general 2D-meshes, Numer. Methods Partial Differential Equations 23 (2007) 145-195. (Pubitemid 46115579)
2. L. Beir̃ao da Veiga, V. Gyrya, K. Lipnikov and G. Manzini, Mimetic finite difference method for the Stokes problem on polygonal meshes, J. Comput. Phys. 228 (2009) 7215-7232.
3. L. Beir̃ao da Veiga and K. Lipnikov, A mimetic discretization of the Stokes problem with selected edge bubbles, SIAM J. Sci. Comp. 32 (2010) 875-893.
4. F. Boyer and F. Hubert, Finite volume method for 2D linear and nonlinear elliptic problems with discontinuities, SIAM J. Numer. Anal. 46 (2008) 3032-3070.
5. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, Vol. 15 (Springer-Verlag, 1991).
6. S. Delcourte, Développement de méthodes de volumes finis pour la mécanique des fluides, Ph.D. thesis, http://tel.archives- ouvertes.fr/tel-00200833/fr/, France (2007).
7. K. Domelevo and P. Omnes, A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN Math. Model. Numer. Anal. 39 (2005) 1203-1249. (Pubitemid 43057983)
8. J. Droniou and R. Eymard, Study of the mixed finite volume method for Stokes and Navier-Stokes equations, Numer. Methods Partial Differential Equations 25 (2009) 137-171.
9. R. Eymard, R. Herbin and J.-C. Latché, On a stabilized colocated finite volume scheme for the Stokes problem, M2AN Math. Model. Numer. Anal. 40 (2006) 501-527. (Pubitemid 44106967)
10. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms, Springer Series in Computational Mathematics (Springer-Verlag, 1986).
11. F. Harlow and J. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids 8 (1965) 2182-2189.
12. F. Hermeline, A finite volume method for the approximation of diffusion operators on distorted meshes, J. Comput. Phys. 160 (2000) 481-499.
13. S. Krell, Finite volume method for general multifluid flows governed by the interface Stokes problem, Technical Report, HAL (2011), http://hal.archives- ouvertes.fr/hal-00473783/fr/.
14. S. Krell, Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes, Numer. Methods Partial Differential Equations 27 (2011) 1666-1706.
15. S. Krell and G. Manzini, The discrete duality finite volume method for the Stokes equation on 3D polyhedral meshes, preprint, (2011), http://hal.archives-ouvertes.fr/hal-00448465/fr/.
16. R. A. Nicolaides, Analysis and convergence of the MAC scheme. I. The linear problem, SIAM J. Numer. Anal. 29 (1992) 1579-1591. (Pubitemid 23606062)
17. K. Ohmori and N. Saito, On the convergence of finite element solutions to the interface problem for the Stokes system, J. Comput. Appl. Math. 198 (2007) 116-128. (Pubitemid 44345055)
18. R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Studies in Mathematics and Its Applications, Vol. 2 (North-Holland, 1977).