EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 47 / No 4 (July-August 2013) ESAIM: M2AN, 47 4 (2013) 1207-1235 References
Free Access
Issue
ESAIM: M2AN
Volume 47, Number 4, July-August 2013
Page(s) 1207 - 1235
DOI https://doi.org/10.1051/m2an/2013069
Published online 17 June 2013
  1. M. Aurada, M. Feischl, J. Kemetmüller, M. Page and D. Praetorius, Each H1 / 2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd(extended preprint) ASC Report 03/2012, Institute for Analysis and Scientific Computing, Vienna University of Technology (2012). [Google Scholar]
  2. M. Aurada, S. Ferraz-Leite and D. Praetorius, Estimator reduction and convergence of adaptive BEM. Appl. Numer. Math. 62 (2012). [Google Scholar]
  3. M. Ainsworth and T. Oden, A posteriori error estimation in finite element analysis, Wiley–Interscience, New-York (2000). [Google Scholar]
  4. S. Bartels, C. Carstensen and G. Dolzmann, Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis. Numer. Math. 99 (2004) 1–24. [CrossRef] [MathSciNet] [Google Scholar]
  5. P. Binev, W. Dahmen and R. DeVore, Adaptive finite element methods with convergence rates, Numer. Math. 97 (2004) 219–268. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Binev, W. Dahmen, R. DeVore and P. Petrushev, Approximation Classes for Adaptive Methods. Serdica. Math. J. 28 (2002) 391–416. [MathSciNet] [Google Scholar]
  7. R. Becker and S. Mao, Convergence and quasi–optimal complexity of a simple adaptive finite element method. ESAIM: M2AN 43 (2009) 1203–1219. [CrossRef] [EDP Sciences] [Google Scholar]
  8. I. Babuška and M. Vogelius, Feedback and adaptive finite element solution of one-dimensional boundary value problems. Numer. Math. 44 (1984) 75–102. [CrossRef] [MathSciNet] [Google Scholar]
  9. C. Carstensen, M. Maischak and E.P. Stephan, A posteriori error estimate and h-adaptive algorithm on surfaces for Symm’s integral equation. Numer. Math. 90 (2001) 197–213. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Cascón, C. Kreuzer, R. Nochetto and K. Siebert: quasi–optimal convergence rate for an adaptive finite element method. SIAM J. Numer. Anal. 46 (2008) 2524–2550. [Google Scholar]
  11. M. Cascón, R. Nochetto: Quasioptimal cardinality of AFEM driven by nonresidual estimators. IMA J. Numer. Anal. 32 (2012) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  12. W. Dörfler: A convergent adaptive algorithm for Poisson’s equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Feischl, M. Karkulik, M. Melenk and D. Praetorius, Quasi–optimal convergence rate for an adaptive boundary element method. SIAM J. Numer. Anal. (2013). [Google Scholar]
  14. M. Feischl, M. Page and D. Praetorius, Convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data, ASC Report 34/2010, Institute for Analysis and Scientific Computing, Vienna University of Technology (2010). [Google Scholar]
  15. F. Gaspoz and P. Morin, Approximation classes for adaptive higher order finite element approximation. To appear in Math. Comput. (2012). [Google Scholar]
  16. George C. Hsiao, Wolfgang and L. Wendland, Boundary Integral Equations. Springer Verlag, Berlin (2008). [Google Scholar]
  17. C. Kreuzer and K. Siebert, Decay rates of adaptive finite elements with Dörfler marking. Numer. Math. 117 (2011) 679–716. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Karkulik, G. Of and D. Praetorius, Convergence of adaptive 3D BEM for some weakly singular integral equations based on isotropic mesh–refinement. Numer. Methods Partial Differ. Eq. (2013). [Google Scholar]
  19. M. Karkulik, D. Pavlicek and D. Praetorius, On 2D newest vertex bisection: Optimality of mesh-closure and H1–stability of L2–projection. Constr. Approx. (2013). [Google Scholar]
  20. W. McLean, Strongly elliptic systems and boundary integral equations. Cambridge University Press, Cambridge (2000). [Google Scholar]
  21. P. Morin, R. Nochetto and K. Siebert, Data oscillation and convergence of adaptive FEM. SIAM J. Numer. Anal. 18 (2000) 466–488. [CrossRef] [MathSciNet] [Google Scholar]
  22. P. Morin, R. Nochetto and K. Siebert, Local problems on stars: a posteriori error estimators, convergence, and performance. Math. Comput. 72 (2003) 1067–1097. [Google Scholar]
  23. P. Morin, K. Siebert and A. Veeser, A basic convergence result for conforming adaptive finite elements. Math. Models Methods Appl. Sci. 18 (2008) 707–737. [Google Scholar]
  24. R. Sacchi and A. Veeser, Locally efficient and reliable a posteriori error estimators for Dirichlet problems. Math. Models Methods Appl. Sci. 16 (2006) 319–346. [CrossRef] [Google Scholar]
  25. S. Sauter and C. Schwab, Randelementmethoden. Springer, Wiesbaden (2004). [Google Scholar]
  26. L. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput 54 (1990) 483–493. [Google Scholar]
  27. R. Stevenson: Optimality of standard adaptive finite element method. Found. Comput. Math. (2007) 245–269. [Google Scholar]
  28. R. Stevenson, The completion of locally refined simplicial partitions created by bisection. Math. Comput. 77 (2008) 227–241. [CrossRef] [MathSciNet] [Google Scholar]
  29. Traxler: An Algorithm for Adaptive Mesh Refinement in n Dimensions. Computing 59 (1997) 115–137. [CrossRef] [MathSciNet] [Google Scholar]
  30. R. Verfürth, A review of a posteriori error estimation and adaptive mesh–refinement techniques. Wiley–Teubner (1996). [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