Free Access
Issue
ESAIM: M2AN
Volume 42, Number 3, May-June 2008
Page(s) 493 - 505
DOI https://doi.org/10.1051/m2an:2008014
Published online 03 April 2008
  1. M. Ainsworth and P. Coggins, A uniformly stable family of mixed hp-finite elements with continuous pressures for incompressible flow. IMA J. Numer. Anal. 22 (2002) 307–327. [CrossRef] [MathSciNet] [Google Scholar]
  2. D.N. Arnold, D. Boffi and R.S. Falk, Approximation by quadrilateral finite elements. Math. Comput. 71 (2002) 909–922. [CrossRef] [MathSciNet] [Google Scholar]
  3. I. Babuška and A. Miller, A feedback finite element method with a posteriori error estimation. I. The finite element method and some basic properties of the a posteriori error estimator. Comput. Methods Appl. Mech. Engrg. 61 (1987) 1–40. [CrossRef] [MathSciNet] [Google Scholar]
  4. C. Bernardi and Y. Maday, Uniform inf-sup conditions for the spectral discretization of the Stokes problem. Math. Models Methods Appl. Sci. 9 (1999) 395–414. [CrossRef] [MathSciNet] [Google Scholar]
  5. D. Boffi and L. Gastaldi, On the quadrilateral Q2-P1 element for the Stokes problem. Int. J. Numer. Methods Fluids 39 (2002) 1001–1011. [CrossRef] [Google Scholar]
  6. J.M. Boland and R.A. Nicolaides, Stability of finite elements under divergence constraints. SIAM J. Numer. Anal. 20 (1983) 722–731. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Bönisch, V. Heuveline and P. Wittwer, Adaptive boundary conditions for exterior flow problems. J. Math. Fluid Mech. 7 (2005) 85–107. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Brezzi and R.S. Falk, Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal. 28 (1991) 581–590. [CrossRef] [MathSciNet] [Google Scholar]
  9. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics 15. Springer-Verlag (1991). [Google Scholar]
  10. L. Chilton and M. Suri, On the construction of stable curvilinear p version elements for mixed formulations of elasticity and Stokes flow. Numer. Math. 86 (2000) 29–48. [CrossRef] [MathSciNet] [Google Scholar]
  11. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes equations. Springer-Verlag, Berlin-Heidelberg-New York (1986). [Google Scholar]
  12. V. Heuveline and M. Hinze, Adjoint-based adaptive time-stepping for partial differential equations using proper orthogonal decomposition. Technical report, University Heidelberg, Germany, SFB 359 (2004). [Google Scholar]
  13. V. Heuveline and R. Rannacher, A posteriori error control for finite element approximations of elliptic eigenvalue problems. Adv. Comput. Math. 15 (2001) 107–138. [CrossRef] [MathSciNet] [Google Scholar]
  14. V. Heuveline and R. Rannacher, Duality-based adaptivity in the hp-finite element method. J. Numer. Math. 11 (2003) 95–113. [CrossRef] [MathSciNet] [Google Scholar]
  15. V. Heuveline and F. Schieweck, H1-interpolation on quadrilateral and hexahedral meshes with hanging nodes. Computing 80 (2007) 203–220. [CrossRef] [MathSciNet] [Google Scholar]
  16. V. Heuveline and F. Schieweck, On the inf-sup condition for higher order mixed fem on meshes with hanging nodes. ESAIM: M2AN 41 (2007) 1–20. [CrossRef] [EDP Sciences] [Google Scholar]
  17. G. Matthies, Mapped finite elements on hexahedra. Necessary and sufficient conditions for optimal interpolation errors. Numer. Algorithms 27 (2001) 317–327. [CrossRef] [MathSciNet] [Google Scholar]
  18. G. Matthies, Finite element methods for free boundary value problems with capillary surfaces. Ph.D. thesis, Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Germany (2002). [Published at Shaker-Verlag Aachen]. [Google Scholar]
  19. G. Matthies and F. Schieweck, On the reference mapping for quadrilateral and hexahedral finite elements on multilevel adaptive grids. Computing 80 (2007) 95–119. [CrossRef] [MathSciNet] [Google Scholar]
  20. G. Matthies and L. Tobiska, The inf-sup condition for the mapped Qk-Formula element in arbitrary space dimensions. Computing 69 (2002) 119–139. [CrossRef] [MathSciNet] [Google Scholar]
  21. S. Schötzau, C. Schwab and R. Stenberg, Mixed hp-fem on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes. Numer. Math. 83 (1999) 667–697. [MathSciNet] [Google Scholar]
  22. C. Schwab, p- and hp-Finite Element Methods, Theory and Applications in Solid and Fluid Mechanics, Numerical Mathematics and Scientific Computation. Oxford Science Publications, Clarendon Press (1998). [Google Scholar]
  23. R. Stenberg, Error analysis of some finite element methods for the Stokes problem. Math. Comput. 54 (1990) 495–508. [CrossRef] [MathSciNet] [Google Scholar]
  24. R. Stenberg and M. Suri, Mixed hp finite element methods for problems in elasticity and Stokes flow. Numer. Math. 72 (1996) 367–389. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Toselli and C. Schwab, Mixed hp-finite element approximations on geometric edge and boundary layer meshes in three dimensions. Numer. Math. 94 (2003) 771–801. [MathSciNet] [Google Scholar]

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