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. [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, 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. [MathSciNet] [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. [CrossRef] [MathSciNet] [PubMed] [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]

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