Free Access
Volume 50, Number 6, November-December 2016
Page(s) 1615 - 1630
Published online 04 October 2016
  1. P.F. Antonietti, A. Dedner, P. Madhavan, S. Stangalino, B. Stinner and M. Verani, High order discontinuous Galerkin methods on surfaces. SIAM J. Numer. Anal. 53 (2015) 1145–1171. [CrossRef] [Google Scholar]
  2. J. Bear, Dynamics of Fluids in Porous Media. American Elsevier (1972). [Google Scholar]
  3. M. Bertalmío, L.-T. Cheng, S. Osher and G. Sapiro, Variational problems and partial differential equations on implicit surfaces. J. Comput. Phys. 174 (2001) 759–780. [CrossRef] [Google Scholar]
  4. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Vol. 15 of Comput. Math. Springer Verlag, Berlin (1991). [Google Scholar]
  5. C.D. Cantwell, S. Yakovlev, R.M. Kirby, N.S. Peters and S.J. Sherwin, High-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: Application to cardiac electrophysiology. J. Comput. Phys. 257 (2014) 813–829. [CrossRef] [PubMed] [Google Scholar]
  6. P.G. Ciarlet, Mathematical Elasticity Volume I: Three-Dimensional Elasticity. Vol. 20 of Stud. Math. Appl. Elsevier (1988). [Google Scholar]
  7. C. D’Angelo and A. Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. Math. Model. Numer. Anal. 46 (2012) 465–489. [Google Scholar]
  8. F. Dassi, S. Perotto, L. Formaggia and P. Ruffo, Efficient geometric reconstruction of complex geological structures. Math. Comput. Simul. 106 (2014) 163–184. [CrossRef] [Google Scholar]
  9. M.C. Delfour and J.-P. Zolésio, Shapes and Geometries, 2nd edition. Society for Industrial and Applied Mathematics (2011). [Google Scholar]
  10. A. Demlow and G. Dziuk, An adaptive finite element method for the Laplace-Beltrami operator on implicitly defined surfaces. SIAM J. Numer. Anal. 45 (2007) 421–442. [CrossRef] [MathSciNet] [Google Scholar]
  11. G. Dziuk, Finite elements for the Beltrami operator on arbitrary surfaces. In Partial Differential Equations and Calculus of Variations. Edited by S. Hildebrandt and R. Leis. Vol. 1357 of Lect. Notes Math. Springer, Berlin, Heidelberg (1988) 142–155. [Google Scholar]
  12. G. Dziuk, and C.M. Elliott, Finite elements on evolving surfaces. IMA J. Numer. Anal. 27 (2007) 262–292. [CrossRef] [MathSciNet] [Google Scholar]
  13. G. Dziuk and C.M Elliott, Surface finite elements for parabolic equations. J. Comput. Math. 25 (2007). [Google Scholar]
  14. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. Applied Mathematical Sciences. Springer (2004). [Google Scholar]
  15. L. Formaggia, A. Fumagalli, A. Scotti and P. Ruffo, A reduced model for Darcy’s problem in networks of fractures. ESAIM: M2AN 48 (2014) 1089–1116. [Google Scholar]
  16. G. Fourestey and S. Deparis, Lifev user manual. Available at November (2010). [Google Scholar]
  17. A. Fumagalli and A. Scotti, A numerical method for two-phase flow in fractured porous media with non-matching grids. Computational Methods in Geologic CO2 Sequestration. Adv. Water Resour. 62 (2013) 454–464. [Google Scholar]
  18. A. Fumagalli and A. Scotti, An efficient XFEM approximation of Darcy flow in arbitrarly fractured porous media. Oil Gas Sci. Technol. – Revue d’IFP Energies Nouvelles 69 (2014) 555–564. [CrossRef] [EDP Sciences] [Google Scholar]
  19. M. Holst and A. Stern, Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces. Found. Comput. Math. 12 (2012) 263–293. [CrossRef] [MathSciNet] [Google Scholar]
  20. V. Martin, J. Jaffré and J.E. Roberts, Modeling fractures and barriers as interfaces for flow in porous media. SIAM J. Sci. Comput. 26 (2005) 1667–1691. [Google Scholar]
  21. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Vol. 23 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1994). [Google Scholar]
  22. M.E. Rognes, R.C Kirby and A. Logg, Efficient assembly of h(div) and h(curl) conforming finite elements. SIAM J. Sci. Comput. 31 (2009) 4130–4151. [CrossRef] [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