Free Access
Issue
ESAIM: M2AN
Volume 36, Number 6, November/December 2002
Page(s) 1043 - 1070
DOI https://doi.org/10.1051/m2an:2003005
Published online 15 January 2003
  1. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney and D. Sorensen, LAPACK Users' Guide. SIAM, Philadelphia, PA, third edition (1999). [Google Scholar]
  2. T. Apel, Anisotropic finite elements: Local estimates and applications. Teubner, Stuttgart, Adv. Numer. Math. (1999). Habilitationsschrift. [Google Scholar]
  3. T. Apel, V. Mehrmann and D. Watkins, Structured eigenvalue methods for the computation of corner singularities in 3D anisotropic elastic structures. Comput. Methods Appl. Mech. Engrg. (to appear), Preprint SFB393/01-25, TU Chemnitz (2001). [Google Scholar]
  4. R.E. Barnhill and J.A. Gregory, Interpolation remainder theory from Taylor expansions on triangles. Numer. Math. 25 (1976) 401-408. [CrossRef] [Google Scholar]
  5. Z.P. Bazant and L.M. Keer, Singularities of elastic stresses and of harmonic functions at conical notches or inclusions. Internat. J. Solids Structures 10 (1974) 957-964. [CrossRef] [Google Scholar]
  6. A.E. Beagles and A.-M. Sändig, Singularities of rotationally symmetric solutions of boundary value problems for the Lamé equations. ZAMM 71 (1990) 423-431. [Google Scholar]
  7. P. Benner, R. Byers, V. Mehrmann and H. Xu, Numerical computation of deflating subspaces of embedded Hamiltonian pencils. SIAM J. Matrix Anal. Appl. (to appear), Preprint SFB393/99-15, TU Chemnitz (1999). [Google Scholar]
  8. M. Costabel and M. Dauge, General edge asymptotics of solutions of second order elliptic boundary value problems I, II. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 109-155, 157-184. [MathSciNet] [Google Scholar]
  9. M. Dauge, Elliptic boundary value problems on corner domains - smoothness and asymptotics of solutions. Lecture Notes in Math. 1341, Springer, Berlin (1988). [Google Scholar]
  10. M. Dauge, Singularities of corner problems and problems of corner singularities, in: Actes du 30ème Congrés d'Analyse Numérique: CANum '98 (Arles, 1998), Soc. Math. Appl. Indust., Paris (1999) 19-40. [Google Scholar]
  11. M. Dauge, ``Simple'' corner-edge asymptotics. Internet publication,http://www.maths.univ-rennes1.fr/~dauge/publis/corneredge.pdf (2000). [Google Scholar]
  12. J.W. Demmel, J.R. Gilbert and X.S. Li, SuperLU Users' Guide. Technical Report LBNL-44289, Lawrence Berkeley National Laboratory (1999). [Google Scholar]
  13. A. Dimitrov, H. Andrä and E. Schnack, Efficient computation of order and mode of corner singularities in 3d-elasticity. Internat. J. Numer. Methods Engrg. 52 (2001) 805-827. [CrossRef] [Google Scholar]
  14. A. Dimitrov and E. Schnack, Asymptotical expansion in non-Lipschitzian domains: a numerical approach using h-fem. Numer. Linear Algebra Appl. (to appear). [Google Scholar]
  15. P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, Boston-London-Melbourne, Monographs and Studies in Mathematics 21 (1985). [Google Scholar]
  16. G. Haase, T. Hommel, A. Meyer, and M. Pester, Bibliotheken zur Entwicklung paralleler Algorithmen. Preprint SPC95_20, TU Chemnitz-Zwickau (1995). Updated version of SPC94_4 and SPC93_1. [Google Scholar]
  17. H. Jeggle and E. Wendland, On the discrete approximation of eigenvalue problems with holomorphic parameter dependence. Proc. Roy. Soc. Edinburgh Sect. A 78 (1977) 1-29. [MathSciNet] [Google Scholar]
  18. O.O. Karma, Approximation of operator functions and convergence of approximate eigenvalues. Tr. Vychisl. Tsentra Tartu. Gosudarst. Univ. 24 (1971) 3-143. In Russian. [Google Scholar]
  19. O.O. Karma, Asymptotic error estimates for approximate characteristic value of holomorphic Fredholm operator functions. Zh. Vychisl. Mat. Mat. Fiz. 11 (1971) 559-568. In Russian. [Google Scholar]
  20. O.O. Karma, Approximation in eigenvalue problems for holomorphic Fredholm operator functions. I. Numer. Funct. Anal. Optim. 17 (1996) 365-387. [CrossRef] [MathSciNet] [Google Scholar]
  21. O.O. Karma, Approximation in eigenvalue problems for holomorphic Fredholm operator functions. II: Convergence rate. Numer. Funct. Anal. Optim. 17 (1996) 389-408. [CrossRef] [MathSciNet] [Google Scholar]
  22. V.A. Kondrat'ev, Boundary value problems for elliptic equations on domains with conical or angular points. Tr. Mosk. Mat. Obs. 16 (1967) 209-292. In Russian. [Google Scholar]
  23. V.A. Kozlov, V.G. Maz'ya and J. Roßmann, Elliptic Boundary Value Problems in Domains with Point Singularities. American Mathematical Society (1997). [Google Scholar]
  24. V.A. Kozlov, V.G. Maz'ya and J. Roßmann, Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations. American Mathematical Society (2001). [Google Scholar]
  25. S.G. Krejn and V.P. Trofimov, On holomorphic operator functions of several complex variables. Funct. Anal. Appl. 3 (1969) 85-86. In Russian. English transl. in Funct. Anal. Appl. 3 (1969) 330-331. [Google Scholar]
  26. S.G. Krejn and V.P. Trofimov, On Fredholm operator depending holomorphically on the parameters. Tr. Seminara po funk. anal. Voronezh univ. (1970) 63-85. [Google Scholar]
  27. D. Leguillon, Computation of 3D-singularities in elasticity, in: Boundary value problems and integral equations in nonsmooth domains, M. Costabel, M. Dauge and S. Nicaise Eds. New York, Lecture Notes in Pure and Appl. Math. 167 (1995) 161-170. Marcel Dekker. Proceedings of a conference at CIRM, Luminy, France, May 3-7 (1993). [Google Scholar]
  28. D. Leguillon and E. Sanchez-Palencia, Computation of singular solutions in elliptic problems and elasticity. Masson, Paris (1987). [Google Scholar]
  29. R.B. Lehoucq, D.C. Sorensen and C. Yang, ARPACK user's guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. SIAM, Philadelphia, PA, Software Environ. Tools 6 (1998). [Google Scholar]
  30. A.S. Markus, On holomorphic operator functions. Dokl. Akad. Nauk 119 (1958) 1099-1102. In Russian. [Google Scholar]
  31. A.S. Markus, Introduction to spectral theory of polynomial operator pencils. American Mathematical Society, Providence (1988). [Google Scholar]
  32. A.S. Markus and E.I. Sigal, The multiplicity of the characteristic number of an analytic operator function. Mat. Issled. 5 (1970) 129-147. In Russian. [MathSciNet] [Google Scholar]
  33. V.G. Maz'ya and B. Plamenevskiĭ, Lp-estimates of solutions of elliptic boundary value problems in domains with edges. Tr. Mosk. Mat. Obs. 37 (1978) 49-93. In Russian. English transl. in Trans. Moscow Math. Soc. 1 (1980) 49-97. [Google Scholar]
  34. V.G. Maz'ya and B. Plamenevskiĭ, The first boundary value problem for classical equations of mathematical physics in domains with piecewise smooth boundaries, part I, II. Z. Anal. Anwendungen 2 (1983) 335-359, 523-551. In Russian. [MathSciNet] [Google Scholar]
  35. V.G. Maz'ya and J. Roßmann, Über die Asymptotik der Lösung elliptischer Randwertaufgaben in der Umgebung von Kanten. Math. Nachr. 138 (1988) 27-53. [CrossRef] [MathSciNet] [Google Scholar]
  36. V.G. Maz'ya and J. Roßmann, On the Agmon-Miranda maximum principle for solutions of elliptic equations in polyhedral and polygonal domains. Ann. Global Anal. Geom. 9 (1991) 253-303. [CrossRef] [MathSciNet] [Google Scholar]
  37. V.G. Maz'ya and J. Roßmann, On the behaviour of solutions to the dirichlet problem for second order elliptic equations near edges and polyhedral vertices with critical angles. Z. Anal. Anwendungen 13 (1994) 19-47. [MathSciNet] [Google Scholar]
  38. V. Mehrmann and D. Watkins, Structure-preserving methods for computing eigenpairs of large sparse skew-Hamiltonian/ Hamiltonian pencils. SIAM J. Sci. Comput. 22 (2001) 1905-1925. [CrossRef] [Google Scholar]
  39. B. Mercier and G. Raugel, Résolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis en r,z et séries de Fourier en θ. RAIRO Anal. Numér. 16 (1982) 405-461. [MathSciNet] [Google Scholar]
  40. S.A. Nazarov and B.A. Plamenevsky, Elliptic problems in domains with piecewise smooth boundary. Walter de Gruyter, Berlin, Exposition. Math. 13 (1994). [Google Scholar]
  41. S. Nicaise, Regularity of the solutions of elliptic systems in polyhedral domains. Bull. Belg. Math. Soc. Simon Stevin 4 (1997) 411-429. [MathSciNet] [Google Scholar]
  42. M. Pester, Grafik-Ausgabe vom Parallelrechner für 2D-Gebiete. Preprint SPC94_24, TU Chemnitz-Zwickau (1994). [Google Scholar]
  43. G. Raugel, Résolution numérique de problèmes elliptiques dans des domaines avec coins. Ph.D. thesis, Université de Rennes, France (1978). [Google Scholar]
  44. G. Raugel, Résolution numérique par une méthode d'éléments finis du problème de Dirichlet pour le Laplacien dans un polygone. C. R. Acad. Sci. Paris Sér. I Math. 286 (1978) A791-A794. [Google Scholar]
  45. A.-M. Sändig and R. Sändig, Singularities of non-rotationally symmetric solutions of boundary value problems for the Lamé equations in a three dimensional domain with conical points. Breitenbrunn, Analysis on manifolds with singularities (1990), Teubner-Texte zur Mathematik, Band 131 (1992) 181-193. [Google Scholar]
  46. H. Schmitz, K. Volk and W.L. Wendland, On three-dimensional singularities of elastic fields near vertices. Numer. Methods Partial Differential Equations 9 (1993) 323-337. [Google Scholar]
  47. V. Staroverov, G. Kobelkov, E. Schnack and A. Dimitrov, On numerical methods for flat crack propagation. IMF-Preprint 99-2, Universität Karlsruhe (1999). [Google Scholar]
  48. V.P. Trofimov, The root subspaces of operators that depend analytically on a parameter. Mat. Issled. 3 (1968) 117-125. In Russian. [MathSciNet] [Google Scholar]
  49. G.M. Vainikko and O.O. Karma, Convergence rate of approximate methods in an eigenvalue problem with a parameter entering nonlinearly. Zh. Vychisl. Mat. Mat. Fiz. 14 (1974) 1393-1408. In Russian. [Google Scholar]

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