Free Access
Issue
ESAIM: M2AN
Volume 51, Number 4, July-August 2017
Page(s) 1367 - 1385
DOI https://doi.org/10.1051/m2an/2016066
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. [CrossRef] [MathSciNet]
  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]
  3. C. Bernardi and V. Girault, A local regularization operator for triangular and quadrilateral finite elements. SIAM J. Numer. Anal. 35 (1998) 1893–1916. [CrossRef] [MathSciNet]
  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. [CrossRef] [MathSciNet]
  5. E. Burman and A. Ern, Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations. Math. Comput. 76 (2007) 1119–1140. [CrossRef] [MathSciNet]
  6. M. Campos Pinto and E. Sonnendrücker, Gauss-compatible Galerkin schemes for time-dependent Maxwell equations. Math. Comput. 302 (2016) 2651–2685. [CrossRef]
  7. P. Ciarlet Jr,, Analysis of the Scott-Zhang interpolation in the fractional order Sobolev spaces. J. Numer. Math. 21 (2013) 173–180. [MathSciNet]
  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).
  9. P. Clément, Approximation by finite element functions using local regularization. RAIRO: Anal. Numer. 9 (1975) 77–84.
  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. [CrossRef] [MathSciNet]
  11. D. Di Pietro and A. Ern, Mathematical aspects of discontinuous Galerkin methods. Vol. 69 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Heidelberg (2012).
  12. T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces. Math. Comput. 34 (1980) 441–463. [CrossRef] [MathSciNet]
  13. A. Ern and J.-L. Guermond, Theory and practice of finite elements. Vol. 159 of Appl. Math. Sci. Springer-Verlag, New York (2004).
  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. [CrossRef] [MathSciNet]
  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]
  16. P. Grisvard, Elliptic problems in nonsmooth domains. Vol. 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985).
  17. N. Heuer, On the equivalence of fractional-order Sobolev semi-norms. J. Math. Anal. Appl. 417 (2014) 505–518. [CrossRef] [MathSciNet]
  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. [CrossRef] [MathSciNet]
  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).
  20. P. Oswald, On a BPX-preconditioner for P1 elements. Computing 51 (1993) 125–133. [CrossRef] [MathSciNet]
  21. A.C. Ponce and J. Van Schaftingen, The continuity of functions with N-th derivative measure. Houston J. Math. 33 (2007) 927–939. [MathSciNet]
  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.
  23. R.L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [CrossRef] [MathSciNet]
  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).

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