Free Access
Issue
ESAIM: M2AN
Volume 46, Number 6, November-December 2012
Page(s) 1467 - 1483
DOI https://doi.org/10.1051/m2an/2012010
Published online 31 May 2012
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Elsevier (2003).
  2. T. Apel, O. Benedix, D. Sirch and B. Vexler, A priori mesh grading for an elliptic problem with Dirac right-hand side. SIAM J. Numer. Anal. 49 (2011) 992–1005. [CrossRef]
  3. R. Araya, E. Behrens and R. Rodríguez. A posteriori error estimates for elliptic problems with Dirac delta source terms. Numer. Math. 105 (2006) 193–216. [CrossRef] [MathSciNet]
  4. D.N. Arnold, An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742–760. [CrossRef] [MathSciNet]
  5. D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 (2001) 1749–1779. [CrossRef] [MathSciNet]
  6. R. Becker and R. Rannacher, An optimal control approach to a-posteriori error estimation in finite element methods, edited by A. Iserles. Cambridge University Press. Acta Numerica (2001) 1–102.
  7. E. Casas, L2 estimates for the finite element method for the Dirichlet problem with singular data. Numer. Math. 47 (1985) 627–632. [CrossRef] [MathSciNet]
  8. M. Dauge, Elliptic Boundary Value Problems on Corner Domains. Lect. Notes Math. 1341 (1988).
  9. J. Douglas and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods, in Computing methods in applied sciences (Second Internat. Sympos., Versailles, 1975). Lect. Notes Phys. 58 (1976) 207–216. [CrossRef]
  10. K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations, edited by A. Iserles. Cambridge University Press. Acta Numerica (1995) 105–158. [CrossRef]
  11. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman (1985).
  12. P. Houston and E. Süli, Adaptive finite element approximation of hyperbolic problems, in Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics, edited by T. Barth and H. Deconinck. Lect. Notes Comput. Sci. Eng. 25 (2002).
  13. P. Houston and T.P. Wihler, Second-order elliptic PDE with discontinuous boundary data. IMA J. Numer. Anal. 32 (2012) 48–74. [CrossRef] [MathSciNet]
  14. V. John, A posteriori L2-error estimates for the nonconforming P1/P0-finite element discretization of the Stokes equations. J. Comput. Appl. Math. 96 (1998) 99–116. [CrossRef] [MathSciNet]
  15. B. Rivière, Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations, Theory and Implementation, in Front. Appl. Math. SIAM (2008).
  16. B. Rivière, M.F. Wheeler and V. Girault, A priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems. SIAM J. Numer. Anal. 39 (2001) 902–931 (electronic). [CrossRef] [MathSciNet]
  17. R. Scott, Finite element convergence for singular data. Numer. Math. 21 (1973/1974) 317–327. [CrossRef] [MathSciNet]
  18. M.F. Wheeler, An elliptic collocation finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152–161. [CrossRef] [MathSciNet]
  19. T.P. Wihler and B. Rivière, Discontinuous Galerkin methods for second-order elliptic PDE with low-regularity solutions. J. Sci. Comput. 46 (2011) 151–165. [CrossRef]

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