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All issues Volume 45 / No 2 (March-April 2011) ESAIM: M2AN, 45 2 (2011) 255-275 References
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Issue
ESAIM: M2AN
Volume 45, Number 2, March-April 2011
Page(s) 255 - 275
DOI https://doi.org/10.1051/m2an/2010039
Published online 02 August 2010
  1. I. Babuška and M. Suri, The h – p version of the finite element method with quasiuniform meshes. RAIRO Modél. Math. Anal. Numér. 21 (1987) 199–238. [MathSciNet] [Google Scholar]
  2. I. Babuška, A. Craig, J. Mandel and J. Pitkäranta, Efficient preconditioning for the p-version finite element method in two dimensions. SIAM J. Numer. Anal. 28 (1991) 624–661. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Bespalov and N. Heuer, Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions. SIAM J. Numer. Anal. 47 (2009) 3977–3989. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Bespalov and N. Heuer, Natural p-BEM for the electric field integral equation on screens. IMA J. Numer. Anal. (2010) DOI:10.1093/imanum/drn072. [Google Scholar]
  5. A. Bespalov and N. Heuer, Thehp – BEMS with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis. Appl. Numer. Math. 60 (2010) 705–718. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bespalov, N. Heuer and R. Hiptmair, Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces. arXiv:0907.5231 (2009). [Google Scholar]
  7. D. Boffi, L. Demkowicz and M. Costabel, Discrete compactness for the p and hp 2D edge finite elements. Math. Models Methods Appl. Sci. 13 (2003) 1673–1687. [Google Scholar]
  8. D. Boffi, M. Costabel, M. Dauge and L. Demkowicz, Discrete compactness for the hp version of rectangular edge finite elements. SIAM J. Numer. Anal. 44 (2006) 979–1004. [CrossRef] [MathSciNet] [Google Scholar]
  9. D. Boffi, M. Costabel, M. Dauge, L. Demkowicz and R. Hiptmair, Discrete compactness for the p -version of discrete differential forms. arXiv:0909.5079 (2009). [Google Scholar]
  10. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics 15. Springer-Verlag, New York (1991). [Google Scholar]
  11. A. Buffa, Remarks on the discretization of some noncoercive operator with applications to heterogeneous Maxwell equations. SIAM J. Numer. Anal. 43 (2005) 1–18. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Buffa and S.H. Christiansen, The electric field integral equation on Lipschitz screens: definitions and numerical approximation. Numer. Math. 94 (2003) 229–267. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Buffa and P. Ciarlet, Jr., On traces for functional spaces related to Maxwell's equations, Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications. Math. Methods Appl. Sci. 24 (2001) 31–48. [Google Scholar]
  14. A. Buffa, R. Hiptmair, T. von Petersdorff and C. Schwab, Boundary element methods for Maxwell transmission problems in Lipschitz domains. Numer. Math. 95 (2003) 459–485. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Costabel and M. Dauge, Singularities of electromagnetic fields in polyhedral domains. Arch. Rational Mech. Anal. 151 (2000) 221–276. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Costabel and A. McIntosh, On Bogovskiĭ and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains. Math. Z. 265 (2010) 297–320. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Costabel, M. Dauge and L. Demkowicz, Polynomial extension operators for H1, H(curl) and H(div)-spaces on a cube. Math. Comp. 77 (2008) 1967–1999. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Demkowicz, Polynomial exact sequences and projection-based interpolation with applications to Maxwell equations, in Mixed Finite Elements, Compatibility Conditions and Applications, D. Boffi, F. Brezzi, L. Demkowicz, R. Duran, R. Falk and M. Fortin Eds., Lect. Notes in Mathematics 1939, Springer-Verlag, Berlin (2008) 101–158. [Google Scholar]
  19. L. Demkowicz and I. Babuška, p interpolation error estimates for edge finite elements of variable order in two dimensions. SIAM J. Numer. Anal. 41 (2003) 1195–1208. [CrossRef] [MathSciNet] [Google Scholar]
  20. M.R. Dorr, The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal. 21 (1984) 1180–1207. [CrossRef] [MathSciNet] [Google Scholar]
  21. N. Heuer, Additive Schwarz method for the p-version of the boundary element method for the single layer potential operator on a plane screen. Numer. Math. 88 (2001) 485–511. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Hiptmair, Discrete compactness for the p-version of tetrahedral edge elements. Seminar for Applied Mathematics, ETH Zürich, Switzerland (2008) arXiv:0901.0761. [Google Scholar]
  23. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I. Springer-Verlag, New York (1972). [Google Scholar]
  24. S.E. Mikhailov, About traces, extensions and co-normal derivative operators on Lipschitz domains, in Integral Methods in Science and Engineering: Techniques and Applications, C. Constanda and S. Potapenko Eds., Birkhäuser, Boston (2008) 149–160. [Google Scholar]
  25. R.E. Roberts and J.-M. Thomas, Mixed and hybrid methods, in Handbook of Numerical Analysis II, P.G. Ciarlet and J.-L. Lions Eds., Amsterdam, North-Holland (1991) 523–639. [Google Scholar]

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