Free Access
Issue
ESAIM: M2AN
Volume 48, Number 6, November-December 2014
Page(s) 1701 - 1724
DOI https://doi.org/10.1051/m2an/2014016
Published online 26 September 2014
  1. D. Aronson, The porous medium equation. Nonlinear Diffusion Problems, edited by A. Fasano, M. Primicerio. Lect. Notes Math. 1224 (1986) 1–46. [Google Scholar]
  2. S.F. Ashby, W.J. Bosl, R.D. Falgout, S.G. Smith, A.F. Tompson and T.J. Williams, A Numerical Simulation of Groundwater Flow and Contaminant Transport on the CRAY T3D and C90 Supercomputers. Int. J. High Performance Comput. Appl. 13 (1999) 80–93. [CrossRef] [Google Scholar]
  3. P. Basser and D. Jones, Diffusion-tensor mri: theory, experimental design and data analysis–a technical review. NMR Biomedicine 15 (2002) 456–467. [CrossRef] [Google Scholar]
  4. C. Beaulieu, The basis of anisotropic water diffusion in the nervous system–a technical review. NMR Biomedicine 15 (2002) 435–455. [Google Scholar]
  5. B. Berkowitz, Characterizing flow and transport in fractured geological media: A review. Adv. Water Resources 25 (2002) 861–884. [Google Scholar]
  6. P. Degond, F. Deluzet, A. Lozinski, J. Narski and C. Negulescu, Duality-based asymptotic-preserving method for highly anisotropic diffusion equations. Commun. Math. Sci. 10 (2012) 1–31. [CrossRef] [Google Scholar]
  7. P. Degond, A. Lozinski, J. Narski and C. Negulescu, An asymptotic-preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition. J. Comput. Phys. 231 (2012) 2724–2740. [CrossRef] [Google Scholar]
  8. Y. Dubinskii, Some integral inequalities and the solvability of degenerate quasi-linear elliptic systems of differential equations. Matematicheskii Sbornik 106 (1964) 458–480. [Google Scholar]
  9. Y. Dubinskii, Weak convergence for nonlinear elliptic and parabolic equations. Matematicheskii Sbornik 109 (1965) 609–642. [Google Scholar]
  10. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Stud. Adv. Math. CRC press (1992). [Google Scholar]
  11. S. Günter, K. Lackner C. Tichmann, Finite element and higher order difference formulations for modelling heat transport in magnetised plasmas. J. Comput. Phys. 226 (2007) 2306–2316. [CrossRef] [Google Scholar]
  12. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Ser. Comput. Math. Springer-Verlag, New York (1987). [Google Scholar]
  13. H. Jian and B. Song, Solutions of the anisotropic porous medium equation in Rn under an l1-initial value. Nonlinear Anal. 64 (2006) 2098–2111. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. SIAM J. Sci. Comput. 21 (1999) 441–454. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Gauthier-Villars (1969). [Google Scholar]
  16. J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I. Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181. Springer-Verlag, New York (1972). [Google Scholar]
  17. H. Lutjens and J. Luciani, The xtor code for nonlinear 3d simulations of mhd instabilities in tokamak plasmas. J. Comput. Phys. 227 (2008) 6944–6966. [CrossRef] [Google Scholar]
  18. A. Mentrelli and C. Negulescu, Asymptotic preserving scheme for highly anisotropic, nonlinear diffusion equations J. Comput. Phys. 231 (2012) 8229–8245. [CrossRef] [Google Scholar]
  19. W. Park, E. Belova, G. Fu, X. Tang, H. Strauss L. Sugiyama, Plasma simulation studies using multilevel physics models. Phys. Plasmas 6 (1999) 1796. [CrossRef] [Google Scholar]
  20. P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion. Pattern Analysis and Machine Intelligence, IEEE Trans. 12 (1990) 629–639. [Google Scholar]
  21. M. Pierre, personal e-mail (2011). [Google Scholar]
  22. J. Narski, Anisotropic finite elements with high aspect ratio for an Asymptotic Preserving method for highly anisotropic elliptic equation. Preprint arXiv:1302.4269 (2013). [Google Scholar]
  23. J. Narski and M. Ottaviani, Asymptotic Preserving scheme for strongly anisotropic parabolic equations for arbitrary anisotropy direction. Preprint arXiv:1303.5219 (2013). [Google Scholar]
  24. J. Simon, Compact sets in the space Lp(0,T;B). Ann. Mat. Pura Appl. 146 (1987) 65–96. [Google Scholar]
  25. P. Tamain, Etude des flux de matière dans le plasma de bord des tokamaks. Ph.D. Thesis, Marseille 1 (2007). [Google Scholar]
  26. J. Vázquez, The porous medium equation: mathematical theory. Oxford University Press, USA (2007). [Google Scholar]
  27. J. Weickert, Anisotropic diffusion in image processing. European Consortium for Mathematics in Industry. B.G. Teubner, Stuttgart (1998). [Google Scholar]
  28. J. Wesson, Tokamaks. Oxford University Press, New York (1987). [Google Scholar]
  29. O.C. Zienkiewicz and R.L. Taylor, The finite element method. Vol. 1. Butterworth-Heinemann, Oxford (2000). [Google Scholar]
  30. J. Wloka, Partial diflerential equations. Cambridge University Press (1987). [Google Scholar]

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