Free Access
Issue
ESAIM: M2AN
Volume 39, Number 6, November-December 2005
Page(s) 1087 - 1114
DOI https://doi.org/10.1051/m2an:2005050
Published online 15 November 2005
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. D.N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. RAIRO Modél. Math. Anal. Numér. 19 (1985) 7–32. [MathSciNet] [Google Scholar]
  3. D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Discontinuous Galerkin methods. Lect. Notes Comput. Sci. Engrg. 11, Springer-Verlag (2000) 89–101. [Google Scholar]
  4. I. Babuska and J. Osborn, Generalized finite element methods, their performance and their relation to mixed methods. SIAM J. Numer. Anal. 20 (1983) 510–536. [CrossRef] [MathSciNet] [Google Scholar]
  5. J. Baranger, J.F. Maitre and F. Oudin, Connection between finite volume and mixed finite element methods. RAIRO Modél. Math. Anal. Numér. 30 (1996) 445–465. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  6. C.L. Bottasso, S. Micheletti and R. Sacco, The Discontinuous Petrov-Galerkin method for elliptic problems. Comput. Methods Appl. Mech. Engrg. 191 (2002) 3391–3409. [CrossRef] [MathSciNet] [Google Scholar]
  7. C.L. Bottasso, S. Micheletti and R. Sacco, A multiscale formulation of the Discontinuous Petrov–Galerkin method for advective-diffusion problems. Comput. Methods Appl. Mech. Engrg. 194 (2005) 2819–2838. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Brezzi, L.D. Marini and P. Pietra, Numerical simulation of semiconductor devices. Comput. Meths. Appl. Mech. Engrg. 75 (1989) 493–514. [CrossRef] [Google Scholar]
  9. F. Brezzi, L.D. Marini and P. Pietra, Two-dimensional exponential fitting and applications to drift-diffusion models. SIAM J. Numer. Anal. 26 (1989) 1342–1355. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Causin, Mixed-hybrid Galerkin and Petrov-Galerkin finite element formulations in fluid mechanics. Ph.D. Thesis, Università degli Studi di Milano (2003). [Google Scholar]
  11. P. Causin and R. Sacco, Mixed-hybrid Galerkin and Petrov-Galerkin finite element formulations in continuum mechanics. in Proc. of the Fifth World Congress on Computational Mechanics (WCCM V), Vienna, Austria. H.A. Mang, F.G. Rammerstorfer and J. Eberhardsteiner Eds., Vienna University of Technology, Austria, http://wccm.tuwien.ac.at, July 7–12 (2002). [Google Scholar]
  12. P. Causin and R. Sacco, A Discontinuous Petrov–Galerkin method with Lagrangian multipliers for second order elliptic problems. SIAM J. Numer. Anal. 43 (2005) 280–302. [CrossRef] [MathSciNet] [Google Scholar]
  13. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North Holland, Amsterdam (1978). [Google Scholar]
  14. B. Cockburn and J. Gopalakhrisnan, A characterization of hybridized mixed methods for second order elliptic problems. SIAM Jour. Numer. Anal. 42 (2003) 283–301. [CrossRef] [Google Scholar]
  15. M. Crouzeix and P.A. Raviart, Conforming and non-conforming finite element methods for solving the stationary Stokes equations. RAIRO, R-3 (1973) 33–76. [Google Scholar]
  16. C. Dawson, Godunov mixed methods for advection-diffusion equations in multidimensions. SIAM J. Numer. Anal. 30 (1993) 1315–1332. [CrossRef] [MathSciNet] [Google Scholar]
  17. C. Dawson and V. Aizinger, Upwind-mixed methods for transport equations. Comp. Geosc. 3 (1999) 93–110. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  18. J. Gopalakhrisnan and G. Kanschat, A multilevel discontinuous galerkin method. Numer. Math. 95 (2003) 527–550. [CrossRef] [MathSciNet] [Google Scholar]
  19. J. Jaffré, Décentrage et éléments finis mixtes pour les équations de diffusion-convection. Calcolo 2 (1984) 171–197. [Google Scholar]
  20. J.W. Jerome, Analysis of Charge Transport. Springer-Verlag, Berlin, Heidelberg (1996). [Google Scholar]
  21. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Dunod (1968). [Google Scholar]
  22. L.D. Marini, An inexpensive method for the evaluation of the solution of the lower order Raviart–Thomas method. SIAM J. Numer. Anal. 22 (1985) 493–496. [CrossRef] [MathSciNet] [Google Scholar]
  23. P.A. Markowich, The Stationary Semiconductor Device Equations. Springer-Verlag, Wien, New York (1986). [Google Scholar]
  24. S. Micheletti, R. Sacco and F. Saleri, On some mixed finite element methods with numerical integration. SIAM J. Sci. Comput. 23 (2001) 245–270. [CrossRef] [MathSciNet] [Google Scholar]
  25. J.J. Miller and S. Wang, A new non-conforming Petrov–Galerkin finite element method with triangular elements for an advection-diffusion problem. IMA J. Numer. Anal. 14 (1994) 257–276. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Mizukami and T.J.R. Hughes, A Petrov-Galerkin finite element method for convection–dominated flows: an accurate upwinding technique satisfying the discrete maximum principle. Comput. Meth. Appl. Mech. Engrg. 50 (1985) 181–193. [CrossRef] [Google Scholar]
  27. K. Ohmori and T. Ushijima, A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations. RAIRO 3 (1984) 309–332. [Google Scholar]
  28. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer-Verlag, New York, Berlin (1994). [Google Scholar]
  29. P.A. Raviart and J.M. Thomas, Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comp. 31-138 (1977) 391–413. [Google Scholar]
  30. J.E. Roberts and J.M. Thomas, Mixed and hybrid methods. In Finite Element Methods, Part I. P.G. Ciarlet and J.L. Lions (Eds.), North-Holland, Amsterdam 2 (1991). [Google Scholar]
  31. H.G. Roos, M. Stynes and L. Tobiska, Numerical methods for singularly perturbed differential equations. Springer-Verlag, Berlin, Heidelberg (1996). [Google Scholar]
  32. R. Sacco, E. Gatti and L. Gotusso, The patch test as a validation of a new finite element for the solution of convection-diffusion equations. Comp. Meth. Appl. Mech. Engrg. 124 (1995) 113–124. [CrossRef] [Google Scholar]
  33. P. Siegel, R. Mosé, Ph. Ackerer and J. Jaffré, Solution of the advection-diffusion equation using a combination of discontinuous and mixed finite elements. Inter. J. Numer. Methods Fluids 24 (1997) 593–613. [Google Scholar]
  34. R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1977). [Google Scholar]

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