Publication Cover
Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 4
84
Views
2
CrossRef citations to date
0
Altmetric
Articles

Local discontinuous Galerkin approximation of non-Fickian diffusion model in viscoelastic polymers

, &
Pages 819-839 | Received 10 Jun 2013, Accepted 11 Mar 2014, Published online: 03 Apr 2014

References

  • Cohen DS, White AB. Sharp fronts due to diffusion and viscoelastic relaxation in polymers. SIAM J. Appl. Math. 1991;51:472–483.
  • Vrentas JS, Duda JL, Hou AC. Anomalous sorption in poly(ethylmethacrylate). J. Appl. Polymer Sci. 1984;29:399–406.
  • Cohen DS, White Jr, AB, Witelski Jr, TP. Shock formation in a multidimensional viscoelastic diffusive system. SIAM J. Appl. Math. 1995;55:348–368.
  • Rivière B, Shaw S. Discontinuous Galerkin finite element approximation of nonlinear non-Fickian diffusion in viscoelastic polymers. SIAM J. Numer. Anal. 2006;44:2650–2670.
  • Bauermeister N, Shaw S. Finite element approximation of non-Fickian polymer diffusion. IMA J. Numer. Anal. 2010;30:702–730.
  • Shaw S. Finite element approximation of a non-local problem in non-Fickian polymer diffusion. Int. J. Numer. Anal. Model. 2011;8:226–251.
  • Cockburn B, Shu CW. The local discontinuous Galerkin method for time-dependent convection diffusion systems. SIAM J. Numer. Anal. 1998;35:2240–2463.
  • Castillo P, Cockburn B, Perugia I, Schötzau D. An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. SIAM J. Numer. Anal. 2000;38:1676–1706.
  • Cockburn B, Kanschat G, Schötzau D, Schwab C. Local discontinuous Galerkin methods for the Stokes system. SIAM J. Numer. Anal. 2002;40:319–343.
  • Cockburn B, Kanschat G, Schötzau D. The local discontinuous Galerkin method for the Oseen equations. Math. Comp. 2004;73:569–593.
  • Cockburn B, Dong B. An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems. J. Sci. Comput. 2007;32:233–262.
  • Xu Y, Shu CW. Local discontinuous Galerkin method for high-order time-dependent partial differential equations. Commun. Comput. Phys. 2010;7:1–46.
  • Pani AK, Yadav S. An hp-local discontinuous Galerkin method for parabolic integro-differential equations. J. Sci. Comput. 2011;46:71–99.
  • Heywood JG, Rannacher R. Finite-element approximation of the nonstationary Navier–Stokes problem. Part IV: Error analysis for second-order time discretization. SIAM J. Numer. Anal. 1990;27:353–384.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.