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Hybrid Galerkin boundary elements on degenerate meshes


Graham, I; Hackbusch, W; Sauter, S (2000). Hybrid Galerkin boundary elements on degenerate meshes. In: Bonnet, M; Sändig, A M; Wendland, W L. Mathematical aspects of boundary element methods (Palaiseau 1998). Boca Raton, FL: Chapman & Hall/CRC, 140-151.

Abstract

In recent work ["Discrete boundary element methods on general meshes in 3D", Bath Mathematics Preprint No. 97/19, Univ. Bath, Bath, 1997; "Hybrid Galerkin boundary elements: theory and implementation", Preprint No. 98-6, Univ. Kiel, Kiel, 1998] we have presented a new discretisation scheme for boundary integral equations which has the same energy norm stability and convergence properties as the Galerkin method but has a complexity comparable with discrete collocation or Nyström methods. Our results were for non-quasiuniform but nevertheless shape-regular meshes. Here we extend the theory to much more general meshes, including the degenerate meshes commonly used to handle singularities arising from corners and edges in 3D applications. As an application we give numerical results for the classical problem of computing the capacitance of a two-dimensional plate in R3. These show that the method is capable of attaining the same type of complexity reduction for singular problems as was already attained for smooth applications in [I. G. Graham, W. Hackbusch and S. A. Sauter, op. cit., 1998].

In recent work ["Discrete boundary element methods on general meshes in 3D", Bath Mathematics Preprint No. 97/19, Univ. Bath, Bath, 1997; "Hybrid Galerkin boundary elements: theory and implementation", Preprint No. 98-6, Univ. Kiel, Kiel, 1998] we have presented a new discretisation scheme for boundary integral equations which has the same energy norm stability and convergence properties as the Galerkin method but has a complexity comparable with discrete collocation or Nyström methods. Our results were for non-quasiuniform but nevertheless shape-regular meshes. Here we extend the theory to much more general meshes, including the degenerate meshes commonly used to handle singularities arising from corners and edges in 3D applications. As an application we give numerical results for the classical problem of computing the capacitance of a two-dimensional plate in R3. These show that the method is capable of attaining the same type of complexity reduction for singular problems as was already attained for smooth applications in [I. G. Graham, W. Hackbusch and S. A. Sauter, op. cit., 1998].

Citations

Additional indexing

Other titles:Dedicated to Vladimir Mazʹya on the occasion of his 60th birthday. Proceedings of the minisymposium held at the École Polytechnique, Palaiseau, May 25–29, 1998
Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2000
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Chapman & Hall/CRC
Series Name:Chapman & Hall/CRC Research Notes in Mathematics
Number:414
ISBN:1-58488-006-6
Official URL:http://www.crcpress.com/product/isbn/9781584880066
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1719856
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0937.65127

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