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All issues Volume 46 / No 5 (September-October 2012) ESAIM: M2AN, 46 5 (2012) 1003-1028 References
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Issue
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
Page(s) 1003 - 1028
DOI https://doi.org/10.1051/m2an/2011046
Published online 13 February 2012
  1. D.N. Arnold, F. Brezzi and M. Fortin, A stable finite element for the Stokes equations. Calcolo 21 (1984) 337–344. [Google Scholar]
  2. 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 (2002) 1749–1779. [CrossRef] [MathSciNet] [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. R. Becker, E. Burman and P. Hansbo, A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity. Comput. Methods Appl. Mech. Engrg. 198 (2009) 3352–3360. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Bercovier and O.A. Pironneau, Error estimates for finite element method solution of the Stokes problem in the primitive variables. Numer. Math. 33 (1977) 211–224. [Google Scholar]
  6. S.C. Brenner, Korn’s inequalities for piecewise H1 vector fields. Math. Comp. 73 (2003) 1067–1087. [CrossRef] [MathSciNet] [Google Scholar]
  7. S.C. Brenner, Poincaré-Friedrichs inequalities for piecewise H1 functions. SIAM J. Numer. Anal. 41 (2003) 306–324. [CrossRef] [MathSciNet] [Google Scholar]
  8. S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, 3th edition, Springer (2008). [Google Scholar]
  9. S.C. Brenner and L.-Y. Sung, Linear finite element methods for planar linear elasticity. Math. Comp. 59 (1992) 321–338. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Brezzi, On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO Anal. Numér. 8 (1974) 129–151. [Google Scholar]
  11. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer Series in Computational Mathematics, Springer-Verlag, New York (1991). [Google Scholar]
  12. F. Brezzi, J. Douglas Jr., and L.D. Marini, Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47 (1985) 217–235. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Brezzi, J. Douglas Jr., R. Durán and M. Fortin, Mixed finite elements for second order elliptic problems in three variables. Numer. Math. 51 (1987) 237–250. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Brezzi, G. Manzini, D. Marini, P. Pietra and A. Russo, Discontinuous galerkin approximations for elliptic problems. Numer. Methods Partial Differential Equations (2000) 365–378. [Google Scholar]
  15. F. Brezzi, T.J.R. Hughes, L.D. Marini and A. Masud, Mixed discontinuous Galerkin methods for Darcy flow. J. Sci. Comput. 22, 23 (2005) 119–145. [CrossRef] [MathSciNet] [Google Scholar]
  16. J. Carrero, B. Cockburn and D. Schötzau, Hybridized globally divergence-free LDG methods. Part I : the Stokes problem. Math. Comp. 75 (2005) 533–563. [Google Scholar]
  17. P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1978). [Google Scholar]
  18. B. Cockburn, G. Kanschat, D. Schötzau and C. Schwab, Local discontinuous Galerkin methods for the Stokes system. SIAM J. Numer. Anal. 40 (2002) 319–343. [CrossRef] [MathSciNet] [Google Scholar]
  19. B. Cockburn, D. Schötzau and J. Wang, Discontinuous Galerkin methods for incompressible elastic materials. Comput. Methods Appl. Mech. Engrg. 195 (2006) 3184–3204. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO Sér. Rouge 7 (1973) 33–75. [Google Scholar]
  21. M. Fortin, An analysis of the convergence of mixed finite element methods. RAIRO Anal. Numér. 11 (1977) 341–354. [MathSciNet] [Google Scholar]
  22. V. Girault, B. Rivière and M.F. Wheeler, A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems. Math. Comp. 74 (2005) 53–84. [Google Scholar]
  23. P. Hansbo and M.G. Larson, Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche’s method. Comput. Methods Appl. Mech. Engrg. 191 (2002) 1895–1908. [CrossRef] [MathSciNet] [Google Scholar]
  24. P. Hansbo and M.G. Larson, Discontinuous Galerkin and the Crouzeix-Raviart element : Application to elasticity. ESAIM : M2AN 37 (2003) 63–72. [Google Scholar]
  25. P. Hansbo and M.G. Larson, Piecewise divergence-free discontinuous Galerkin methods for Stokes flow. Comm. Num. Methods Engrg. 24 (2008) 355–366. [CrossRef] [Google Scholar]
  26. F. Hecht, Construction d’une base de fonctions P1 non conforme à divergence nulle dans R3. RAIRO Anal. Numér. 15 (1981) 119–150. [MathSciNet] [Google Scholar]
  27. P. Hood and C. Taylor, Numerical solution of the Navier-Stokes equations using the finite element technique. Comput. Fluids 1 (1973) 1–28. [CrossRef] [Google Scholar]
  28. P. Hood and C. Taylor, Navier-Stokes equations using mixed interpolation. Finite Element Methods in Flow Problems, edited by J.T. Oden. UAH Press, Huntsville, Alabama (1974). [Google Scholar]
  29. R. Kouhia and R. Stenberg, A linear nonconforming finite element method for nearly incompressible elasticity and Stokes flow. Comput. Methods Appl. Mech. Engrg. 124 (1995) 195–212. [CrossRef] [MathSciNet] [Google Scholar]
  30. A. Lew, P. Neff, D. Sulsky and M. Ortiz, Optimal BV estimates for a discontinuous Galerkin method for linear elasticity. Appl. Math. Res. express 3 (2004) 73–106. [CrossRef] [Google Scholar]
  31. N.C. Nguyen, J. Peraire and B. Cockburn, A hybridizable discontinuous Galerkin method for Stokes flow. Comput. Methods Appl. Mech. Engrg. 199 (2010) 582–597. [CrossRef] [MathSciNet] [Google Scholar]
  32. B. Rivière and V. Girault, Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces. Comput. Methods Appl. Mech. Engrg. 195 (2006) 3274–3292. [CrossRef] [MathSciNet] [Google Scholar]
  33. D. Schötzau, C. Schwab and A. Toselli, Mixed hp-DGFEM for incompressible flows. SIAM J. Numer. Anal. 40 (2003) 2171–2194. [Google Scholar]
  34. L.R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. RAIRO Modélisation Mathématique et Analyse Numérique 19 (1985) 111–143. [Google Scholar]
  35. S.-C. Soon, B. Cockburn and H.K. Stolarski, A hybridizable discontinuous Galerkin method for linear elasticity. Int. J. Numer. Methods Engrg. 80 (2009), 1058–1092. [CrossRef] [Google Scholar]
  36. A. Ten Eyck, and A. Lew, Discontinuous Galerkin methods for non-linear elasticity. Int. J. Numer. Methods Engrg. 67 (2006) 1204–1243. [CrossRef] [Google Scholar]
  37. A. Ten Eyck, F. Celiker and A. Lew, Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity : Analytical estimates. Comput. Methods Appl. Mech. Engrg. 197 (2008) 2989–3000. [CrossRef] [MathSciNet] [Google Scholar]
  38. F. Thomasset, Implementation of finite element methods for Navier-Stokes equations. Springer-Verlag, New York (1981). [Google Scholar]
  39. J.P. Whiteley, Discontinuous Galerkin finite element methods for incompressible non-linear elasticity, Comput. Methods Appl. Mech. Engrg. 198 (2009) 3464–3478. [CrossRef] [Google Scholar]
  40. T.P. Wihler, Locking-free DGFEM for elasticity problems in polygons. IMA J. Numer. Anal. 24 (2004) 45–75. [CrossRef] [MathSciNet] [Google Scholar]

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