Free Access
Volume 48, Number 3, May-June 2014
Page(s) 753 - 764
Published online 01 April 2014
  1. M. Ainsworth, A posteriori error estimation for discontinuous Galerkin finite element approximation. SIAM J. Numer. Anal. 39 (2007) 1777–1798. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis. Pure and Applied Mathematics. Wiley-Interscience, John Wiley & Sons, New York (2000). [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. 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 (2002) 1749–1779. [CrossRef] [MathSciNet] [Google Scholar]
  5. B. Ayuso and L.L. Zikatanov, Uniformly convergent iterative methods for discontinuous Galerkin discretizations. J. Sci. Comput. 40 (2009) 4–36. [CrossRef] [MathSciNet] [Google Scholar]
  6. I. Babuška and I. Strouboulis, The Finite Element Method and its Reliability. The Claredon Press, Oxford University Press (2001) [Google Scholar]
  7. W. Bangerth and R. Rannacher, Adaptive Finite Element Methods for Differential Equations. Birkhåuser Verlag, Basel (2003). [Google Scholar]
  8. F. Bassi, S. Rebay, G. Mariotti, S. Pedinotti, and M. Savini, A higher order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows, in Proc. of 2nd European Conference on Turbomachinery, Fluid Dynamics and Thermodynamics, edited by R. Decuypere and G. Dilbelius, Technologisch Instituut, Antewerpen, Belgium (1997) 99–108. [Google Scholar]
  9. R. Becker, S. Mao and Z.C. Shi, A convergent nonconforming adaptive finite element method with quasi-optimal complexity. SIAM J. Numer. Anal. 47 (2010) 4639–4659. [CrossRef] [Google Scholar]
  10. R. Becker and S. Mao, Private Communication (2013). [Google Scholar]
  11. P. Binev, W. Dahmen, and R. DeVore, Adaptive finite element methods with convergence rates. Numer. Math. 97 (2004) 219–268. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Bonito and R.H. Nochetto, Quasi-optimal convergence rate of an adaptive discontinuous Galerkin method. SIAM J. Numer. Anal. 48 (2010) 734–771. [CrossRef] [Google Scholar]
  13. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3rd edn. Springer-Verlag, New York (2008). [Google Scholar]
  14. S.C. Brenner and L. Owens, A weakly over-penalized non-symmetric interior penalty method. J. Numer. Anal. Ind. Appl. Math. 2 (2007) 35–48. [Google Scholar]
  15. S.C. Brenner, L. Owens and L.Y. Sung, A weakly over-penalized symmetric interior penalty method. Electron. Trans. Numer. Anal. 30 (2008) 107–127. [MathSciNet] [Google Scholar]
  16. F. Brezzi, G. Manzini, D. Marini, P. Pietra and A. Russo, Discontiuous Galerkin Approximations for Elliptic Problems. Numer. Methods Partial Differ. Equ. 16 (2000) 365–378. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Burman and B. Stamm, Low order discontinuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47 (2008) 508–533. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Carstensen and R.H.W. Hoppe, Convergence analysis of an adaptive nonconforming finite element method. Numer. Math. 103 (2006) 251–266. [CrossRef] [MathSciNet] [Google Scholar]
  19. C. Carstensen and R. Hoppe, Error reduction and convergence for an adaptive mixed finite element method. Math. Comput. 75 (2006) 1033–1042. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.M. Cascon, C. Kreuzer, R.H. Nochetto and K.G. Siebert, Quasi-optimal convergence rate for an adaptive finite element method. SIAM J. Numer. Anal. 46 (2008) 2524–2550. [Google Scholar]
  21. L. Chen, M. Holst and J. Xu, Convergence and optimality of adaptive mixed finite element methods. Math. Comput. 78 (2009) 35–53. [CrossRef] [Google Scholar]
  22. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440–2463. [CrossRef] [MathSciNet] [Google Scholar]
  23. M. Crouzeix and P.A. Raviart, Conforming and Nonconforming finite element methods for solving the stationary Stokes equations. RAIRO Anal. Numer. 7 (1973) 33–76. [Google Scholar]
  24. W. Dörfler, A convergent adaptive algorithm for Poisson’s equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. Douglas, Jr. and T. Dupont, Interior penalty procedures for elliptic and parabolic Galerkin methods. In vol. 58. Lect. Notes Phys. Springer-Verlag, Berlin (1976). [Google Scholar]
  26. R.H.W. Hoppe, G. Kanschat and T. Warburton, Convergence analysis ofan adaptive interior penalty discontinuous Galerkin method. SIAM J. Numer. Anal. 47 (2008/09) 534–550. [CrossRef] [Google Scholar]
  27. O. A. Karakashian and F. Pascal, Convergence of adaptive discontinuous Galerkin approximations of second-order elliptic problems. SIAM J. Numer. Anal. 45 (2007) 641–665. [CrossRef] [MathSciNet] [Google Scholar]
  28. S. Mao, X. Zhao and Z. Shi, Convergence of a standard adaptive nonconforming finite element method with optimal complexity. Appl. Numer. Math. 60 (2010) 673–688. [CrossRef] [Google Scholar]
  29. P. Morin, R.H. Nochetto and K.G. Siebert, Data oscillation and convergence adaptive FEM. SIAM J. Numer. Anal. 38 (2000) 466–488. [CrossRef] [MathSciNet] [Google Scholar]
  30. P. Morin, R.H. Nochetto and K.G. Siebert, Convergence of adaptive finite element methods. SIAM Review 44 (2002) 631–658. [Google Scholar]
  31. R. Stevenson, Optimality of a standard adaptive finite element method. Found. Comput. Math. 7 (2007) 245–269. [CrossRef] [MathSciNet] [Google Scholar]
  32. R. Verfürth, A Review of A Posteriori Error Estmation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, Chichester (1995). [Google Scholar]
  33. M.F. Wheeler, An elliptic collocation-finite-element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152–161. [CrossRef] [MathSciNet] [Google Scholar]

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