EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 47 / No 6 (November-December 2013) ESAIM: M2AN, 47 6 (2013) 1845-1864 References
Free Access
Issue
ESAIM: M2AN
Volume 47, Number 6, November-December 2013
Page(s) 1845 - 1864
DOI https://doi.org/10.1051/m2an/2013091
Published online 07 October 2013
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. E. Barkai, Fractional Fokker-Planck equation, solution, and application. Phys. Rev. E. 63 (2001) 046118. [CrossRef] [Google Scholar]
  3. F. Bassi and S. Rebay, A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131 (1997) 267–279. [CrossRef] [MathSciNet] [Google Scholar]
  4. P.L. Butzer and U. Westphal, An Introduction to Fractional Calculus. World Scientific, Singapore (2000). [Google Scholar]
  5. C.-M. Chen, F. Liu, I. Turner and V. Anh, A Fourier method for the fractional diffusion equation describing sub-diffusion. J. Comput. Phys. 227 (2007) 886–897. [CrossRef] [Google Scholar]
  6. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440–2463. [CrossRef] [MathSciNet] [Google Scholar]
  7. P. Castillo, B. Cockburn, D. Schötzau and C. Schwab, Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-diffusion problem. Math. Comput. 71 (2001) 455–478. [Google Scholar]
  8. P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1975). [Google Scholar]
  9. W.H. Deng, Numerical algorithm for the time fractional Fokker-Planck equation. J. Comput. Phys. 227 (2007) 1510–1522. [CrossRef] [Google Scholar]
  10. W.H. Deng, Finite element method for the space and time fractional Fokker-Planck equation. SIAM J. Numer. Anal. 47 (2008) 204–226. [CrossRef] [Google Scholar]
  11. V.J. Ervin and J.P. Roop, Variational formulation for the stationary fractional advection dispersion equation. Numer. Methods Partial Differ. Eqs. 22 (2005) 558–576. [Google Scholar]
  12. J.S. Hesthaven and T. Warburton, High-order nodal discontinuous Galerkin methods for Maxwell eigenvalue problem. Roy. Soc. London Ser. A 362 (2004) 493–524. [CrossRef] [Google Scholar]
  13. J.S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer-Verlag, New York, USA (2008). [Google Scholar]
  14. X. Ji and H. Tang, High-order accurate Runge-Kutta (Local) discontinuous Galerkin methods for one- and two-dimensional fractional diffusion equations. Numer. Math. Theor. Meth. Appl. 5 (2012) 333–358. [CrossRef] [Google Scholar]
  15. C.P. Li and W.H. Deng, Remarks on fractional derivatives. Appl. Math. Comput. 187 (2007) 777–784. [CrossRef] [Google Scholar]
  16. X.J. Li and C.J. Xu, A space-time spectral method for the time fractional diffusion equation. SIAM J. Numer. Anal. 47 (2009) 2108–2131. [Google Scholar]
  17. Y.M. Lin and C.J. Xu, Finite difference/spectral approximations for the time-fractional diffusion equation. J. Comput. Phys. 225 (2007) 1533–1552. [CrossRef] [MathSciNet] [Google Scholar]
  18. W. McLean and K. Mustapha, Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation. Numer. Algorithms 52 (2009) 69–88. [CrossRef] [MathSciNet] [Google Scholar]
  19. K. Mustapha and W. McLean, Discontinuous Galerkin method for an evolution equation with a memory term of positive type. Math. Comput. 78 (2009) 1975–1995. [CrossRef] [Google Scholar]
  20. K. Mustapha and W. McLean, Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation. Numer. Algorithms 56 (2011) 159–184. [CrossRef] [MathSciNet] [Google Scholar]
  21. K. Mustapha and W. McLean, Superconvergence of a discontinuous Galerkin method for the fractional diffusion and wave equation, arXiv:1206.2686v1 (2012). [Google Scholar]
  22. R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 (2000) 1–77. [NASA ADS] [CrossRef] [Google Scholar]
  23. C. Tadjeran and M.M. Meerschaert, A second-order accurate numerical method for the two-dimensional fractional diffusion equation. J. Comput. Phys. 220 (2007) 813–823. [CrossRef] [Google Scholar]
  24. J. Yan and C.-W. Shu, A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40 (2002) 769–791. [CrossRef] [MathSciNet] [Google Scholar]

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