Abstract
We consider an h-adaptive algorithm for the boundary element method applied to two integral equations of the first kind on polygons, namely Symm's integral equation and the hypersingular equation with the normal derivative of the double layer potential. Our reliable and operative algorithm is based on new a posteriori estimates for the boundary element Galerkin solution. Numerical experiments show the effectivity of the algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asadzadch, M.; Eriksson, K. 1994: An adaptive finite element method for the potential problem. SIAM J. Numer. Anal. 31: 831–855
Babuška, I; Miller, A. 1981: A posteriori error estimates and adaptive techniques for the finite element method. Univ. of Maryland, Institute for Physical Science and Technology Tech. Note BN-968, College Park, MD
Carstensen, C.; Stephan, E. P. 1993a: Adaptive boundary element method for transmission problems. Preprint Institute für Angewandte Mathematik, Universität Hannover
Carstensen, C.; Stephan, E. P. 1993b: Adaptive coupling of boundary and finite elements. Preprint Institut für Angewandte Mathematik, Universität Hannover
Carstensen, C.; Stephan, E. P. 1994a: A posteriori error estimates for boundary element methods. Math. Comp. (accepted for publication)
Carstensen, C.; Stephan, E. P. 1994b: Adaptive boundary element methods for some first kind integral equations. SIAM J. Numer. Anal. (accepted for publication)
Costabel, M. 1988: Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Math. Anal. 19: 613–626
Costabel, M.; Stephan, E. P. 1963: The normal derivative of the double layer potential on polygons and Galerkin approximation. Appl. Anal. 16: 205–228
Costabel, M.; Stephan, E. P. 1985: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation. Banach Center Publ. 15: 175–251
Eriksson, K.; Johnson, C. 1988: An adaptive finite element method for linear elliptic problems. Math. Comp. 50: 361–383
Eriksson, K.; Johnson, C. 1991: Adaptive finite element methods for parabolic problems I. A linear model problem SIAM J. Numer. Anal. 28: 43–77
Ervin, V.; Heuer, N.; Stephan, E. P. 1983: On the h-p version of the boundary element method for Symm's integral equation on polygons. Comput. Meth. Appl. Mech. Engin. 110: 25–38
Johnson, C.; Hansbo, P. 1992: Adaptive finite element method in computational mechanics. Comput. Meth. Appl. Mech. Engin. 101: 143–181
Lions, J. L.; Magenes, E. 1972: Non-Homogeneous Boundary Values Problems and Applications I, Berlin, Heidelberg: Springer-Verlag
Postell, F. V.; Stephan, E. P. 1990: On the h-, p- and h-p versions of the boundary element method—numerical results. Computer Meth. in Appl. Mechanics and Egin. 83: 69–89
Rank, E. 1987: Adaptive boundary element methods. In: Brebbia, C. A.; Wendland, W. L.; Kuhn, G. (eds.): Boundary Elements 9, Vol. 1, 259–273. Heidelberg: Springer-Verlag
Wendland, W. L.; Yu, De-hao 1988: Adaptive boundary element methods for strongly elliptic integral equations. Numer. Math. 53: 539–558
Author information
Authors and Affiliations
Additional information
Communicated by H. Antes and T. A. Cruse, 26 July 1994
This work is partly supported by DFG research group at the University of Hannover.
Rights and permissions
About this article
Cite this article
Carstensen, C., Estep, D. & Stephan, P. h-adaptive boundary element schemes. Computational Mechanics 15, 372–383 (1995). https://doi.org/10.1007/BF00372275
Issue Date:
DOI: https://doi.org/10.1007/BF00372275