Free access
Issue
ESAIM: M2AN
Volume 43, Number 6, November-December 2009
Page(s) 1203 - 1219
DOI http://dx.doi.org/10.1051/m2an/2009036
Published online 21 August 2009
  1. I. Babuška and W.C. Rheinboldt, Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978) 736–754. [CrossRef] [MathSciNet]
  2. R. Becker and S. Mao, An optimally convergent adaptive mixed finite element method. Numer. Math. 111 (2008) 35–54. [CrossRef] [MathSciNet]
  3. R. Becker and D. Trujillo, Convergence of an adaptive finite element method on quadrilateral meshes. Research Report RR-6740, INRIA, France (2008).
  4. R. Becker, C. Johnson and R. Rannacher, Adaptive error control for multigrid finite element methods. Computing 55 (1995) 271–288. [CrossRef] [MathSciNet]
  5. R. Becker, S. Mao and Z.-C. Shi, A convergent adaptive finite element method with optimal complexity. Electron. Trans. Numer. Anal. 30 (2008) 291–304. [MathSciNet]
  6. P. Binev, W. Dahmen and R. DeVore, Adaptive finite element methods with convergence rates. Numer. Math. 97 (2004) 219–268. [CrossRef] [MathSciNet]
  7. J.H. Bramble and J.E. Pasciak, New estimates for multilevel algorithms including the v-cycle. Math. Comp. 60 (1995) 447–471.
  8. C. Carstensen, Quasi-interpolation and a posteriori error analysis in finite element methods. ESAIM: M2AN 33 (1999) 1187–1202. [CrossRef] [EDP Sciences]
  9. C. Carstensen and R. Verfürth, Edge residuals dominate a posteriori error estimates for low order finite element methods. SIAM J. Numer. Anal. 36 (1999) 1571–1587. [CrossRef] [MathSciNet]
  10. J.M. Cascon, Ch. Kreuzer, R.N. Nochetto and K.G. Siebert, Quasi-optimal convergence rate for an adaptive finite element method. SIAM J Numer. Anal. 46 (2008) 2524–2550. [CrossRef] [MathSciNet]
  11. P.G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications 4. Amsterdam, New York, Oxford: North-Holland Publishing Company (1978).
  12. A. Cohen, W. Dahmen and R. DeVore, Adaptive wavelet methods for elliptic operator equations: Convergence rates. Math. Comput. 70 (2001) 27–75.
  13. R. DeVore, Nonlinear approximation. Acta Numer. 7 (1998) 51–150. [CrossRef]
  14. W. Dörfler, A convergent adaptive algorithm for Poisson's equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [CrossRef] [MathSciNet]
  15. W. Dörfler and R.H. Nochetto, Small data oscillation implies the saturation assumption. Numer. Math. 91 (2002) 1–12. [CrossRef] [MathSciNet]
  16. K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations. Acta Numer. 4 (1995) 105–158. [CrossRef]
  17. P. Morin, R.H. Nochetto and K.G. Siebert, Data oscillation and convergence of adaptive FEM. SIAM J. Numer. Anal. 38 (2000) 466–488. [CrossRef] [MathSciNet]
  18. P. Morin, K.G. Siebert and A. Veeser, A basic convergence result for conforming adaptive finite elements. Math. Models Methods Appl. Sci. 18 (2008) 707–737. [CrossRef] [MathSciNet] [PubMed]
  19. R. Stevenson, Optimality of a standard adaptive finite element method. Found. Comput. Math. 7 (2007) 245–269. [CrossRef] [MathSciNet]
  20. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. John Wiley/Teubner, New York-Stuttgart (1996).
  21. H. Wu and Z. Chen, Uniform convergence of multigrid v-cycle on adaptively refined finite element meshes for second order elliptic problems. Sci. China Ser. A 49 (2006) 1405–1429. [CrossRef] [MathSciNet]

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