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All issues Volume 48 / No 4 (July-August 2014) ESAIM: M2AN, 48 4 (2014) 1117-1145 References
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Issue
ESAIM: M2AN
Volume 48, Number 4, July-August 2014
Page(s) 1117 - 1145
DOI https://doi.org/10.1051/m2an/2013134
Published online 04 July 2014
  1. Th. Apel, Interpolation of non-smooth functions on anisotropic finite element meshes. ESAIM: M2AN 33 (1999) 1149–1185. [CrossRef] [EDP Sciences] [Google Scholar]
  2. Th. Apel and M. Dobrowolski, Anisotropic interpolation with applications to the finite element method. Computing 47 (1992) 277–293. [CrossRef] [MathSciNet] [Google Scholar]
  3. Th. Apel and B. Heinrich, Mesh refinement and windowing near edges for some elliptic problem. SIAM J. Numer. Anal. 31 (1994) 695–708. [CrossRef] [Google Scholar]
  4. Th. Apel and S. Nicaise, The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges. Math. Methods Appl. Sci. 21 (1998) 519–549. [CrossRef] [MathSciNet] [Google Scholar]
  5. Th. Apel, A.-M. Sändig, and J.R. Whiteman, Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains. Math. Methods Appl. Sci. 19 (1996) 63–85. [CrossRef] [MathSciNet] [Google Scholar]
  6. Th. Apel and D. Sirch, L2-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes. Appl. Math. 56 (2011) 177–206. [CrossRef] [MathSciNet] [Google Scholar]
  7. Th. Apel and D. Sirch, A priori mesh grading for distributed optimal control problems, in Constrained Optimization and Optimal Control for Partial Differential Equations, vol. 160. Edited by G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich, and S. Ulbrich. Int. Ser. Numer. Math.. Springer, Basel (2011) 377–389. [Google Scholar]
  8. F. Assous, P. Ciarlet, Jr. and J. Segré, Numerical solution to the time-dependent Maxwell equations in two-dimensional singular domains: the Singular Complement Method. J. Comput. Phys. 161 (2000) 218–249. [CrossRef] [MathSciNet] [Google Scholar]
  9. I. Babuška, Finite element method for domains with corners. Computing 6 (1970) 264–273. [CrossRef] [Google Scholar]
  10. A.E. Beagles and J.R. Whiteman, Finite element treatment of boundary singularities by augmentation with non-exact singular functions. Numer. Methods Partial Differ. Eqs. 2 (1986) 113–121. [CrossRef] [Google Scholar]
  11. H. Blum and M. Dobrowolski, On finite element methods for elliptic equations on domains with corners. Computing 28 (1982) 53–63. [CrossRef] [MathSciNet] [Google Scholar]
  12. C. Băcuţă, V. Nistor and L.T. Zikatanov, Improving the rate of convergence of high-order finite elements in polyhedra II: mesh refinements and interpolation. Numer. Funct. Anal. Optim. 28 (2007) 775–824. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Buffa, M. Costabel and M. Dauge, Algebraic convergence for anisotropic edge elements in polyhedral domains. Numer. Math. 101 (2005) 29–65. [CrossRef] [MathSciNet] [Google Scholar]
  14. P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numer. 2 (1975) 77–84. [Google Scholar]
  15. T. Dupont and R. Scott, Polynomial approximation of functions in Sobolev spaces. Math. Comput. 34 (1980) 441–463. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. Grisvard, Singularities in boundary value problems, vol. 22. Research Notes Appl. Math. Springer, New York (1992). [Google Scholar]
  17. M. Hinze. A variational discretization concept in control constrained optimization: The linear-quadratic case. Comput. Optim. Appl. 30 (2005) 45–61. [Google Scholar]
  18. P. Jamet, Estimations d’erreur pour des éléments finis droits presque dégénérés. R.A.I.R.O. Anal. Numer. 10 (1976) 43–61. [Google Scholar]
  19. V. John and G. Matthies, MooNMD-a program package based on mapped finite element methods. Comput. Visual. Sci. 6 (2004) 163–169. [CrossRef] [Google Scholar]
  20. F. Kikuchi, On a discrete compactness property for the nédélec finite elements. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (1989) 479–490. [MathSciNet] [Google Scholar]
  21. A.L. Lombardi, The discrete compactness property for anisotropic edge elements on polyhedral domains. ESAIM: M2AN 47 (2013) 169–181. [CrossRef] [EDP Sciences] [Google Scholar]
  22. J. M.-S. Lubuma and S. Nicaise, Dirichlet problems in polyhedral domains II: approximation by FEM and BEM. J. Comput. Appl. Math. 61 (1995) 13–27,. [CrossRef] [Google Scholar]
  23. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press, New York (2003). [Google Scholar]
  24. J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson et Cie, Éditeurs, Paris, Academia, Éditeurs, Paris, Prague (1967). [Google Scholar]
  25. S. Nicaise, Edge elements on anisotropic meshes and approximation of the Maxwell equations. SIAM J. Numer. Anal. 39 (2001) 784–816. [CrossRef] [MathSciNet] [Google Scholar]
  26. L.A. Oganesyan and L.A. Rukhovets, Variational-difference schemes for linear second-order elliptic equations in a two-dimensional region with piecewise smooth boundary. Zh. Vychisl. Mat. Mat. Fiz. 8 (1968) 97–114. In Russian. English translation in USSR Comput. Math. and Math. Phys. 8 (1968) 129–152. [Google Scholar]
  27. T. von Petersdorff and E.P. Stephan. Regularity of mixed boundary value problems in ℝ3 and boundary element methods on graded meshes. Math. Methods Appl. Sci. 12 (1990) 229–249. [CrossRef] [MathSciNet] [Google Scholar]
  28. G. Raugel, Résolution numérique de problèmes elliptiques dans des domaines avec coins. Ph.D. thesis. Université de Rennes (1978). [Google Scholar]
  29. A.H. Schatz and L.B. Wahlbin, Maximum norm estimates in the finite element method on plane polygonal domains. Part 2: Refinements. Math. Comput. 33 (1979) 465–492. [Google Scholar]
  30. H. Schmitz, K. Volk and W.L. Wendland, On three-dimensional singularities of elastic fields near vertices. Numer. Methods Partial Differ. Eqs. 9 (1993) 323–337. [CrossRef] [MathSciNet] [Google Scholar]
  31. L.R. Scott and S. Zhang, Finite element interpolation of non-smooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  32. K. Siebert, An a posteriori error estimator for anisotropic refinement. Numer. Math. 73 (1996) 373–398. [CrossRef] [MathSciNet] [Google Scholar]
  33. G. Strang and G. Fix, An analysis of the finite element method. Prentice-Hall, Englewood Cliffs, NJ (1973). [Google Scholar]

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