Free access
Issue
ESAIM: COCV
Volume 14, Number 4, October-December 2008
Page(s) 802 - 824
DOI http://dx.doi.org/10.1051/cocv:2008011
Published online 30 January 2008
  1. B.A. Andreianov, M. Gutnic and P. Wittbold, Convergence of finite volume approximations for a nonlinear elliptic-parabolic problem: a “continuous" approach. SIAM J. Numer. Anal. 42 (2004) 228–251. [CrossRef] [MathSciNet]
  2. D.N. Arnold, An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742–760. [CrossRef] [MathSciNet]
  3. D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2001-2002) 1749–1779.
  4. J.P. Aubin, Approximation des problèmes aux limites non homogènes pour des opérateurs non linéaires. J. Math. Anal. Appl. 30 (1970) 510–521. [CrossRef] [MathSciNet]
  5. I. Babuška, The finite element method with penalty. Math. Comp. 27 (1973) 221–228. [CrossRef] [MathSciNet]
  6. I. Babuška and M. Zlámal, Nonconforming elements in the finite element method with penalty. SIAM J. Numer. Anal. 10 (1973) 863–875. [CrossRef] [MathSciNet]
  7. I. Babuška, C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for diffusion problems: 1-D analysis. Comput. Math. Appl. 37 (1999) 103–122. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  8. C.E. Baumann and J.T. Oden, Advances and applications of discontinuous Galerkin methods in CFD. Computational mechanics (Buenos Aires, 1998), Centro Internac. Métodos Numér. Ing., Barcelona (1998).
  9. C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 175 (1999) 311–341. [CrossRef] [MathSciNet]
  10. C.E. Baumann and J.T. Oden, An adaptive-order discontinuous Galerkin method for the solution of the Euler equations of gas dynamics. Internat. J. Numer. Methods Engrg. 47 (2000) 61–73. [CrossRef] [MathSciNet]
  11. H. Brezis, Analyse fonctionnelle: Théorie et applications. Masson, Paris (1983).
  12. P.G. Ciarlet, The finite element method for elliptic problems. North Holland, Amsterdam (1978).
  13. P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of numerical analysis, P.G. Ciarlet and J.-L. Lions Eds., North Holland, Amsterdam (1991).
  14. 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]
  15. B. Cockburn, G.E. Karniadakis and C.-W. Shu, The development of discontinuous Galerkin methods, in Discontinuous Galerkin methods (Newport, RI, 1999), Lect. Notes Comput. Sci. Eng. 11 (2000) 3–50.
  16. B. Dacorogna, Direct methods in the calculus of variations. Springer-Verlag, New York (1989).
  17. G. Dal Maso, An introduction to Γ-convergence. Birkäuser, Boston (1993).
  18. C. Davini, Piece-wise constant approximations in the membrane problem. Meccanica 38 (2003) 555–569. [CrossRef] [MathSciNet]
  19. C. Davini and F. Jourdan, Approximations of degree zero in the Poisson problem. Comm. Pure Appl. Anal. 4 (2005) 267–281. [CrossRef]
  20. C. Davini and R. Paroni, Generalized Hessian and external approximations in variational problems of second order. J. Elasticity 70 (2003) 149–174. [CrossRef] [MathSciNet]
  21. C. Davini and R. Paroni, Error estimate of piece-wise constant approximations to the Poisson problem (in preparation).
  22. C. Davini and I. Pitacco, Relaxed notions of curvature and a lumped strain method for elastic plates. SIAM J. Numer. Anal. 35 (1998) 677–691. [CrossRef] [MathSciNet]
  23. C. Davini and I. Pitacco, An unconstrained mixed method for the biharmonic problem. SIAM J. Numer. Anal. 38 (2000) 820–836. [CrossRef] [MathSciNet]
  24. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics. CRC Press, Boca Raton (1992).
  25. J.-L. Lions, Problèmes aux limites non homogènes à données irrégulières : Une méthode d'approximation, in Numerical Analysis of Partial Differential Equations (C.I.M.E. 2 Ciclo, Ispra, 1967), Edizioni Cremonese, Rome (1968) 283–292.
  26. J. NeFormula as, Équations aux dérivées partielles. Presses de l'Université de Montréal (1965).
  27. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9–15. [CrossRef] [MathSciNet]
  28. W.H. Reed and T.R. Hill, Triangular mesh method for neutron transport equation. Tech. Report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos (1973).
  29. M.F. Wheeler, An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152–161. [CrossRef] [MathSciNet]
  30. X. Ye, A new discontinuous finite volume method for elliptic problems. SIAM J. Numer. Anal. 42 (2004) 1062–1072. [CrossRef] [MathSciNet]