Free Access
Volume 50, Number 4, July-August 2016
Page(s) 1193 - 1222
Published online 14 July 2016
  1. M. Ainsworth and R. Rankin, Technical note: A note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes. Numer. Methods Partial Differ. Eq. 28 (2012) 1099–1104. [CrossRef] [Google Scholar]
  2. M. Amara, R. Djellouli and C. Farhat, Convergence analysis of a discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of Helmholtz problems. SIAM J. Numer. Anal. 47 (2009) 1038–1066. [CrossRef] [MathSciNet] [Google Scholar]
  3. D.N. Arnold, An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742–760. [CrossRef] [MathSciNet] [Google Scholar]
  4. I. Babuška and M. Zlámal, Nonconforming elements in the finite element method with penalty. SIAM J. Numer. Anal. 10 (1973) 863–875. [CrossRef] [MathSciNet] [Google Scholar]
  5. G.A. Baker, Finite element methods for elliptic equations using nonconforming elements. Math. Comput. 31 (1977) 45–59. [CrossRef] [MathSciNet] [Google Scholar]
  6. C.E. Baumann and J.T. Oden, A discontinuous hp finite element method for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 175 (1999) 311–341. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Douglas, Jr. and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin Methods. Computing Methods in Applied Sciences (Second Internat. Sympos., Versailles, 1975). In vol. 58 of Lect. Notes Phys. (1976) 207–216. [Google Scholar]
  8. Y. Epshteyn and B. Rivière, Estimation of penalty parameters for symmetric interior penalty Galerkin methods. J. Comput. Appl. Math. 206 (2007) 843–872. [CrossRef] [MathSciNet] [Google Scholar]
  9. M.J. Frisch, J.A. Pople and J.S. Binkley, Self-consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets. J. Chem. Phys. 80 (1984) 3265–3269. [NASA ADS] [CrossRef] [Google Scholar]
  10. S. Giani and E.J.C. Hall, An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. Math. Models Methods Appl. Sci. 22 (2012) 1250030–1250064. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Henning and M. Ohlberge, Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems. Discrete Contin. Dyn. Systems Series S 8 (2015) 119–150. [Google Scholar]
  12. R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version. SIAM J. Numer. Anal. 49 (2011) 264–284. [CrossRef] [MathSciNet] [Google Scholar]
  13. T.Y. Hou and X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169–189. [CrossRef] [MathSciNet] [Google Scholar]
  14. P. Houston, C. Schwab and E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002) 2133–2163. [CrossRef] [MathSciNet] [Google Scholar]
  15. P. Houston, D. Schötzau and T.P. Wihler, Energy norm a posteriori error estimation of hp-adaptive discontinuous Galerkin methods for elliptic problems. Math. Models Methods Appl. Sci. 17 (2007) 33–62. [CrossRef] [MathSciNet] [Google Scholar]
  16. J. Junquera, O. Paz, D. Sanchez-Portal and E. Artacho, Numerical atomic orbitals for linear-scaling calculations. Phys. Rev. B 64 (2001) 235111–235119. [CrossRef] [Google Scholar]
  17. 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] [Google Scholar]
  18. J. Kaye, L. Lin and C. Yang, A posteriori error estimator for adaptive local basis functions to solve Kohn–Sham density functional theory. Commun. Math. Sci. 13 (2015) 1741–1773. [CrossRef] [MathSciNet] [Google Scholar]
  19. A.V. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method. SIAM J. Sci. Comp. 23 (2001) 517. [CrossRef] [Google Scholar]
  20. L. Lin, J. Lu, L. Ying and W. E, Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation. J. Comput. Phys. 231 (2012) 2140–2154. [CrossRef] [Google Scholar]
  21. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36 (1971) 9–15. [Google Scholar]
  22. M. Ohlberger, A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems. Multiscale Model. Simul. 4 (2005) 88–114. [Google Scholar]
  23. M. Ohlberger and F. Schindler, A-posteriori error estimates for the localized reduced basis multi-scale method. In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Edited by J. Fuhrmann, M. Ohlberger and Ch. Rohde. Vol. 77 of Springer Proc. Math. Stat. Springer International Publishing (2014) 421–429. [Google Scholar]
  24. D. Schötzau and L. Zhu, A robust a posteriori error estimator for discontinuous Galerkin methods for convection–diffusion equations. Appl. Numer. Math. 59 (2009) 2236–2255. [CrossRef] [MathSciNet] [Google Scholar]
  25. C. Schwab, p-and hp-Finite Element Methods. Oxford University Press, New York (1998). [Google Scholar]
  26. B. Stamm and T. Wihler, hp-Optimal discontinuous Galerkin methods for linear elliptic problems. Math. Comput. 79 (2010) 2117–2133. [Google Scholar]
  27. R. Tezaur and C. Farhat, Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems. Int. J. Numer. Meth. Eng. 66 (2006) 796–815. [CrossRef] [Google Scholar]
  28. W. E and B. Engquist, The heterognous multiscale methods. Commun. Math. Sci. 1 (2003) 87–132. [CrossRef] [MathSciNet] [Google Scholar]
  29. M.F. Wheeler, An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152–161. [CrossRef] [MathSciNet] [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