Free Access
Issue
ESAIM: M2AN
Volume 49, Number 4, July-August 2015
Page(s) 977 - 990
DOI https://doi.org/10.1051/m2an/2014062
Published online 19 June 2015
  1. J. Alberty, C. Carstensen and S.A. Funken, Remarks around 50 lines of Matlab: short finite element implementation. Numer. Algorithms 20 (1999) 117–137. [Google Scholar]
  2. G.A. Baker, Finite element methods for elliptic equations using nonconforming elements. Math. Comp. 31 (1977) 45–59. [Google Scholar]
  3. P. Binev, W. Dahmen and R. DeVore, Adaptive finite element methods with convergence rates. Numer. Math. 97 (2004) 219–268. [CrossRef] [MathSciNet] [Google Scholar]
  4. D. Braess, An a posteriori error estimate and a comparison theorem for the nonconforming P1 element. Calcolo 46 (2009) 149–155. [CrossRef] [MathSciNet] [Google Scholar]
  5. S.C. Brenner, and L.-Y. Sung, C0 interior penalty methods for fourth order elliptic boundary value problems on polygonal domains. J. Sci. Comput. 22/23 (2005) 83–118. [Google Scholar]
  6. S.C. Brenner, T. Gudi and L.-Y. Sung, An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem. IMA J. Numer. Anal. 30 (2010) 777–798. [CrossRef] [MathSciNet] [Google Scholar]
  7. C. Carstensen, D. Gallistl and J. Hu, A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles. Numer. Math. 124 (2013) 309–335. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Carstensen, D. Gallistl and J. Hu, A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes. Comput. Math. Appl. 68 (2014) 2167–2181. [CrossRef] [Google Scholar]
  9. C. Carstensen, D. Peterseim and M. Schedensack, Comparison results of finite element methods for the Poisson model problem. SIAM J. Numer. Anal. 50 (2012) 2803–2823. [CrossRef] [Google Scholar]
  10. P.G. Ciarlet, The finite element method for elliptic problems. Vol. 4. of Stud. Math. Appl. North-Holland Publishing Co., Amsterdam (1978). [Google Scholar]
  11. G. Engel, K. Garikipati, T.J.R. Hughes, M.G. Larson, L. Mazzei and R.L. Taylor, Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity. Comput. Methods Appl. Mech. Engrg. 191 (2002) 3669–3750. [CrossRef] [MathSciNet] [Google Scholar]
  12. X. Feng and O.A. Karakashian, Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn–Hilliard equation of phase transition. Math. Comp. 76 (2007) 1093–1117. [CrossRef] [MathSciNet] [Google Scholar]
  13. E.H. Georgoulis, P. Houston and J. Virtanen, An a posteriori error indicator for discontinuous Galerkin approximations of fourth-order elliptic problems. IMA J. Numer. Anal. 31 (2011) 281–298. [CrossRef] [MathSciNet] [Google Scholar]
  14. P. Grisvard, Singularities in boundary value problems. Vol. 22 of Recherches en Mathématiques Appliquées [Research in Applied Mathematics]. Masson, Paris (1992). [Google Scholar]
  15. T. Gudi, A new error analysis for discontinuous finite element methods for linear elliptic problems. Math. Comp. 79 (2010) 2169–2189. [Google Scholar]
  16. J. Hu, Z. Shi and J. Xu, Convergence and optimality of the adaptive Morley element method. Numer. Math. 121 (2012) 731–752. [CrossRef] [MathSciNet] [Google Scholar]
  17. I. Mozolevski and E. Süli, A priori error analysis for the hp-version of the discontinuous Galerkin finite element method for the biharmonic equation. Comput. Methods Appl. Math. 3 (2003) 596–607. [CrossRef] [MathSciNet] [Google Scholar]
  18. R. Stevenson, The completion of locally refined simplicial partitions created by bisection. Math. Comp. 77 (2008) 227–241. [Google Scholar]
  19. A. Veeser, Approximating gradients with continuous piecewise polynomial functions. Found. Comput. Math. (2015). Doi: 10.1007/s10208-015-9262-z [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