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A-priori estimates of the hp-adaptive BEM in elastic scattering of acoustic waves

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Warianty tytułu
Konferencja
Polish Conference on Computer methods in mechanics ; (14 ; 26-28.05.1999 ; Rzeszów, Poland
Języki publikacji
EN
Abstrakty
EN
In the paper some a-priori hp-adaptive error estimates, applied to the problem of acoustic wave scattering on an elastic body in the 2D space, solved by the Boundary Element Method, are presented. The estimate includes both the function- and boundary approximation errors.
Rocznik
Strony
559--570
Opis fizyczny
Bibliogr. 20 poz., rys.
Twórcy
autor
  • Cracow University of Technology [Politechnika Krakowska], ul. Warszawska 24, 31-155 Kraków, Poland
Bibliografia
  • [1] S. Amini. On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem. Aplicable Anal., 35: 79-92, 1990.
  • [2] I. Babuśka, M. Dorr. Error estimates for the combined h and p version of the finite element method. Numer. Math., 37: 257-277, 1981.
  • [3] I. Babuśka, B. Q. Guo, E. P. Stephan. On the exponential convergence of the h-p version for Boundary Element Galerkin Methods on polygons. Math. Methods Appl. Sci., 12: 413-427, 1990.
  • [4] I. Babuśka, M. Sufi. The h-p version of the finite element method with quasiuniform meshes, RAIRO, Math. Mod. Numer. Anal., 21: 199-238, 1987.
  • [5] I. Babuśka, M. Sufi. The optimal convergence rate of the p-version of the finite element method. SIAM J. Numer. Anal., 24: 750-776, 1987.
  • [6] L. Demkowicz, J. T. Oden, M. Ainsworth, P. Geng. Solution of elastic scattering problems in linear acoustics using h-p boundary element methods. J. Comput. Appl. Math., 36: 29-63, 1991.
  • [7] V. J. Ervin, N. Heuer, E. P. Stephan. On the h-p version of the Boundary Element Method for Symm's integral equation on polygons. Comput. Methods Appl. Mech. Engrg., 110: 25-38, 1993.
  • [8] N. Heuer, E. P. Stephan, The hp- Version of the Boundary Element Method. ZAMM, 74: T511-T513, 1994.
  • [9] N. Heuer. hp- Versionen der Randelernentmethode. Ph.D. Thesis. Universitat Hannover, Hannover 1992.
  • [10] A. Karafiat. An Analysis of the Boundary Element Method for the Acoustic Scattering Problem (in Polish). Cracow University of Technology, Kraków, 1996.
  • [11] A. Karafiat. On hp- error estimation in the BEM for a three-dimensional Helmholtz exterior problem. Comput. Methods Appl. Mech. Engrg., 150: 199-214, 1997.
  • [12] A. Karafiat, J. T. Oden, P. Geng. Variational formulations and hp Boundary Element Approximations for hypersingular integral equations for Helmholtz exterior boundary value problems in two dimensions. Int. J. Engrg. Sci., 31(4): 649-672, 1993.
  • [13] A. Karafiat. Some mathematical aspects of the BEM in elastic scattering of acoustic waves. In: Proceedings of the IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics, May 30-June 3, 1999, Cracow, Poland (to appear).
  • [14] N. N. Lebedev. Special Functions and their Applications (in Russian). Fizmatgiz, Moscow-Leningrad 1963.
  • [15] M. Maischak, P. Mund, E.P. Stephan. Adaptive multilevel BEM for acoustic scattering. Comput. Methods Appl. Mech. Engrg., 150: 351-367, 1997.
  • [16] M. Maischak. hp- Methoden fur Randintegralgleichungen bei 3D-Problemen, Theorie und Irnplernentierung. Ph.D. Thesis, Universit5,t Hannover, Hannover, 1995.
  • [17] F. V. Postell, E. P. Stephan. On the h, p, and h-p versions of the Boundary Element Method - Numerical results. Comput. Methods Appl. Mech. Engrg., 83: 69-90, 1990.
  • [18] E. Rank. Adaptive h-p-, and hp- versions for boundary integral element methods. Internat. J. Numer. Methods Engrg., 28: 1335-1349, 1989.
  • [19] E. P. Stephan. The h-p Boundary Element Method for solving 2- and 3-dimensional problems. Comput. Methods Appl. Mech. Engrg., 133: 183-208, 1996.
  • [20] W. L. Wendland. Boundary element methods and their asymptotic convergence. In: P. Filippi ed., Theoretical acoustics and numerical treatment, CISM Courses and Lectures, 135-216, Springer, Wien, 1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0005-0034
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