Free Access
Volume 42, Number 3, May-June 2008
Page(s) 493 - 505
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. [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. [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. [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]

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