Free Access
Issue
ESAIM: M2AN
Volume 46, Number 5, September-October 2012
Page(s) 1147 - 1173
DOI https://doi.org/10.1051/m2an/2011075
Published online 13 February 2012
  1. M. Ainsworth and J.T. Oden, A posteriori error estimation in finite element analysis. Wiley-Interscience, John Wiley & Sons, New-York (2000). [Google Scholar]
  2. M. Aurada, P. Goldenits and D. Praetorius, Convergence of data perturbed adaptive boundary element methods. ASC Report 40/2009, Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien (2009). [Google Scholar]
  3. M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr and D. Praetorius, HILBERT – A Matlab implementation of adaptive 2D-BEM. ASC Report 24/2011, Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien (2011). Software download at http://www.asc.tuwien.ac.at/abem/hilbert/. [Google Scholar]
  4. M. Aurada, S. Ferraz-Leite and D. Praetorius, Estimator reduction and convergence of adaptive BEM. Appl. Numer. Math., in print (2011). [Google Scholar]
  5. I. Babuśka 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]
  6. R. Bank, Hierarchical bases and the finite element method. Acta Numer. 5 (1996) 1–45. [CrossRef] [Google Scholar]
  7. F. Bornemann, B. Erdmann and R. Kornhuber, A-posteriori error-estimates for elliptic problems in 2 and 3 space dimensions. SIAM J. Numer. Anal. 33 (1996) 1188–1204. [CrossRef] [MathSciNet] [Google Scholar]
  8. C. Carstensen, An a posteriori error estimate for a first-kind integral equation. Math. Comp. 66 (1997) 139–155. [CrossRef] [MathSciNet] [Google Scholar]
  9. C. Carstensen and D. Praetorius, Averaging techniques for the effective numerical solution of Symm’s integral equation of the first kind. SIAM J. Sci. Comput. 27 (2006) 1226–1260. [CrossRef] [Google Scholar]
  10. C. Carstensen and D. Praetorius, Averaging techniques for the a posteriori BEM error control for a hypersingular integral Equation in two dimensions. SIAM J. Sci. Comput. 29 (2007) 782–810. [CrossRef] [Google Scholar]
  11. C. Carstensen and D. Praetorius, Averaging techniques for a posteriori error control in finite element and boundary element analysis, in Boundary Element Analysis : Mathematical Aspects and Applications, edited by M. Schanz and O. Steinbach. Lect. Notes Appl. Comput. Mech. 29 (2007) 29–59. [CrossRef] [Google Scholar]
  12. C. Carstensen and D. Praetorius, Convergence of adaptive boundary element methods. ASC Report 15/2009, Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien (2009). [Google Scholar]
  13. C. Carstensen and E. Stephan, Adaptive coupling of boundary elements and finite elements. ESAIM : M2AN 29 (1995) 779–817. [Google Scholar]
  14. M. Costabel, A symmetric method for the coupling of finite elements and boundary elements, in The Mathematics of Finite Elements and Applications IV, MAFELAP 1987, edited by J. Whiteman, Academic Press, London (1988) 281–288. [Google Scholar]
  15. P. Deuflhard, P. Leinen and H. Yserentant, Concepts of an adaptive hierarchical finite element code. Impact Comput. Sci. Eng. 1 (1989) 3–35. [CrossRef] [Google Scholar]
  16. W. Dörfler, A convergent adaptive algorithm for Poisson’s equation. SIAM J. Numer. Anal. 33 (1996) 1106–1124. [CrossRef] [MathSciNet] [Google Scholar]
  17. W. Dörfler and R. Nochetto, Small data oscillation implies the saturation assumption. Numer. Math. 91 (2002) 1–12. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Erath, S. Ferraz-Leite, S. Funken and D. Praetorius, Energy norm based a posteriori error estimation for boundary element methods in two dimensions. Appl. Numer. Math. 59 (2009) 2713–2734. [CrossRef] [Google Scholar]
  19. C. Erath, S. Funken, P. Goldenits and D. Praetorius, Simple error estimators for the Galerkin BEM for some hypersingular integral equation in 2D. ASC Report 20/2009, Institute for Analysis and Scientific Computing, Vienna University of Technology, Wien (2009). [Google Scholar]
  20. S. Ferraz-Leite and D. Praetorius, Simple a posteriori error estimators for the h-version of the boundary element method. Computing 83 (2008) 135–162. [CrossRef] [MathSciNet] [Google Scholar]
  21. S. Ferraz-Leite, C. Ortner and D. Praetorius, Convergence of simple adaptive Galerkin schemes based on hh / 2 error estimators. Numer. Math. 116 (2010) 291–316. [CrossRef] [MathSciNet] [Google Scholar]
  22. I. Graham, W. Hackbusch and S. Sauter, Finite elements on degenerate meshes : Inverse-type inequalities and applications. IMA J. Numer. Anal. 25 (2005) 379–407. [CrossRef] [MathSciNet] [Google Scholar]
  23. E. Hairer, S. Nørsett and G. Wanner, Solving ordinary differential equations I, Nonstiff problems. Springer, New York (1987). [Google Scholar]
  24. M. Maischak, P. Mund and E. Stephan, Adaptive multilevel BEM for acoustic scattering. Comput. Methods Appl. Mech. Eng. 150 (2001) 351–367. [CrossRef] [Google Scholar]
  25. W. McLean, Strongly elliptic systems and boundary integral equations. Cambridge University Press, Cambridge (2000). [Google Scholar]
  26. 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. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. P. Mund and E. Stephan, An additive two-level method for the coupling of nonlinear FEM-BEM equations. SIAM J. Numer. Anal. 36 (1999) 1001–1021. [CrossRef] [MathSciNet] [Google Scholar]
  28. P. Mund, E. Stephan and J. Weiße, Two-level methods for the single layer potential in R3. Computing 60 (1998) 243–266. [CrossRef] [MathSciNet] [Google Scholar]
  29. S. Rjasanov and O. Steinbach, The fast solution of boundary integral equations. Springer, New York (2007). [Google Scholar]
  30. S. Sauter and C. Schwab, Randelementmethoden : Analyse, Numerik und Implementierung schneller Algorithmen. Teubner Verlag, Wiesbaden (2004). [Google Scholar]
  31. O. Steinbach, Numerical approximation methods for elliptic boundary value problems : Finite and boundary elements. Springer, New York (2008). [Google Scholar]
  32. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Teubner, Stuttgart (1996). [Google Scholar]
  33. E. Zeidler, Nonlinear functional analysis and its applications. part II/B, Springer, New York (1990). [Google Scholar]

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