Free Access
Volume 51, Number 4, July-August 2017
Page(s) 1367 - 1385
Published online 21 July 2017
  1. Y. Achdou, C. Bernardi and F. Coquel, A priori and a posteriori analysis of finite volume discretizations of Darcy’s equations. Numer. Math. 96 (2003) 17–42. [Google Scholar]
  2. D.N. Arnold, R.S. Falk and R. Winther, Finite element exterior calculus, homological techniques, and applications. Acta Numer. 15 (2006) 1–155. [CrossRef] [MathSciNet] [Google Scholar]
  3. C. Bernardi and V. Girault, A local regularization operator for triangular and quadrilateral finite elements. SIAM J. Numer. Anal. 35 (1998) 1893–1916. [Google Scholar]
  4. J.H. Bramble and S.R. Hilbert, Estimation of linear functionals on Sobolev spaces with application to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970) 112–124. [Google Scholar]
  5. E. Burman and A. Ern, Continuous interior penalty -finite element methods for advection and advection-diffusion equations. Math. Comput. 76 (2007) 1119–1140. [Google Scholar]
  6. M. Campos Pinto and E. Sonnendrücker, Gauss-compatible Galerkin schemes for time-dependent Maxwell equations. Math. Comput. 302 (2016) 2651–2685. [Google Scholar]
  7. P. Ciarlet Jr,, Analysis of the Scott-Zhang interpolation in the fractional order Sobolev spaces. J. Numer. Math. 21 (2013) 173–180. [MathSciNet] [Google Scholar]
  8. P.G. Ciarlet, The finite element method for elliptic problems, Vol. 40 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM). Reprint of the 1978 original [North-Holland, Amsterdam; MR0520174 (58 #25001)]. Philadelphia, PA (2002). [Google Scholar]
  9. P. Clément, Approximation by finite element functions using local regularization. RAIRO: Anal. Numer. 9 (1975) 77–84. [Google Scholar]
  10. B. Cockburn, G. Kanschat and D. Schötzau, A note on discontinuous Galerkin divergence-free solutions of the Navier-Stokes equations. J. Sci. Comput. 31 (2007) 61–73. [Google Scholar]
  11. D. Di Pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods. Vol. 69 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Heidelberg (2012). [Google Scholar]
  12. T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces. Math. Comput. 34 (1980) 441–463. [Google Scholar]
  13. A. Ern and J.-L. Guermond, Theory and practice of finite elements. Vol. 159 of Appl. Math. Sci. Springer-Verlag, New York (2004). [Google Scholar]
  14. A. Ern, A.F. Stephansen and M. Vohralík, Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. J. Comput. Appl. Math. 234 (2010) 114–130. [Google Scholar]
  15. V. Girault and J.-L. Lions, Two-grid finite-element schemes for the transient Navier-Stokes problem. ESAIM: M2AN 35 (2001) 945–980. [CrossRef] [EDP Sciences] [Google Scholar]
  16. P. Grisvard, Elliptic problems in nonsmooth domains. Vol. 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
  17. N. Heuer, On the equivalence of fractional-order Sobolev semi-norms. J. Math. Anal. Appl. 417 (2014) 505–518. [Google Scholar]
  18. O.A. Karakashian and F. Pascal, A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems. SIAM J. Numer. Anal. 41 (2003) 2374–2399. [Google Scholar]
  19. C.B. Morrey, Jr, Mettre en romain : Multiple integrals in the calculus of variations. Die Grundlehren der Mathematischen Wissenschaften, Band 130. Springer-Verlag New York, Inc., New York (1966). [Google Scholar]
  20. P. Oswald, On a BPX-preconditioner for elements. Computing 51 (1993) 125–133. [CrossRef] [MathSciNet] [Google Scholar]
  21. A.C. Ponce and J. Van Schaftingen, The continuity of functions with -th derivative measure. Houston J. Math. 33 (2007) 927–939. [MathSciNet] [Google Scholar]
  22. J. Schöberl and C. Lehrenfeld, Domain decomposition preconditioning for high order hybrid discontinuous Galerkin methods on tetrahedral meshes. In Advanced finite element methods and applications. Vol. 66 of Lect. Notes Appl. Comput. Mech. Springer, Heidelberg (2013) 27–56. [Google Scholar]
  23. R.L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  24. L. Tartar, An introduction to Sobolev spaces and interpolation spaces. Vol. 3 of Lecture Notes of the Unione Matematica Italiana. Springer, Berlin; UMI, Bologna (2007). [Google Scholar]

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