Free Access
Issue
ESAIM: M2AN
Volume 41, Number 1, January-February 2007
Page(s) 1 - 20
DOI https://doi.org/10.1051/m2an:2007005
Published online 26 April 2007
  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. I. Babuška and M. Suri, The p and h - p versions of the finite element method, basic principles and properties. SIAM Rev. 36 (1994) 578–632. [CrossRef] [MathSciNet] [Google Scholar]
  3. C. Bernardi and Y. Maday. Approximations spectrales de problèmes aux limites elliptiques. (Spectral approximation for elliptic boundary value problems). Mathématiques & Applications, Paris, Springer-Verlag 10 (1992). [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, Springer-Verlag 15 (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. P.G. Ciarlet, The finite element method for elliptic problems. Studies in Mathematics and its Applications 4, Amsterdam - New York - Oxford: North-Holland Publishing Company (1978). [Google Scholar]
  12. M. Fortin, An analysis of the convergence of mixed finite element methods. RAIRO Anal. Numer. 11 (1977) 341–354. [Google Scholar]
  13. V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations. Springer-Verlag, Berlin-Heidelberg-New York (1986). [Google Scholar]
  14. V. Heuveline and M. Hinze, Adjoint-based adaptive time-stepping for partial differential equations using proper orthogonal decomposition. Technical report, University Heidelberg, SFB 359 (2004). [Google Scholar]
  15. 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]
  16. 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]
  17. V. Heuveline and F. Schieweck, An interpolation operator for H1 functions on general quadrilateral and hexahedral meshes with hanging nodes. Technical report, University Heidelberg, SFB 359 (2004). [Google Scholar]
  18. 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]
  19. 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]
  20. 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]
  21. Ch. Schwab, p- and hp-finite element methods. Theory and applications in solid and fluid mechanics. Numerical Mathematics and Scientific Computation, Oxford: Clarendon Press (1998). [Google Scholar]
  22. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54 (1990) 483–493. [Google Scholar]
  23. R. Stenberg, Error analysis of some finite element methods for the Stokes problem. Math. Comp. 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. L. Stupelis, Navier-Stokes equations in irregular domains. Mathematics and its Applications 326, Dordrecht: Kluwer Academic Publishers (1995). [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