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SIAM J. on Scientific Computing / Volume 34 / Issue 1 / Methods and Algorithms for Scientific Computing

SIAM J. Sci. Comput. 34, pp. A28-A47 (20 pages)

Coupling at a Distance HDG and BEM

Bernardo Cockburn, Francisco-Javier Sayas, and Manuel Solano

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We introduce a new technique for numerically solving exterior Dirichlet boundary-value problems for second-order elliptic equations. It consists of coupling a hybridizable discontinuous Galerkin (HDG) method used for solving the so-called interior problem on a bounded region containing the support of the source term, with a boundary element method (BEM) for solving the problem exterior to that region. The novelty is that the BEM is defined on a suitably chosen, smooth artificial boundary whereas the HDG method is defined on a polyhedral subdomain. Because of the choice of the artificial boundary, we can take advantage of the spectral convergence of the BEM solution and of the simplicity of the corresponding equations. Because the HDG method is defined on a polyhedral subdomain, there is no need to try to fit the mesh to the artificial boundary. Instead, the HDG is coupled at a distance with the BEM by using simple Dirichlet-to-Neumann operators defined in the region between the artificial boundary and the polyhedral subdomain. Numerical experiments displaying the performance of the new technique are presented. Optimal orders of convergence are obtained even though the distance between the artificial boundary and the polyhedral domain is of order $h$.

© 2012 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

65N30, 65M60

PUBLICATION DATA

ISSN

1064-8275 (print)  
1095-7197 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received February 03, 2011
Accepted September 22, 2011
Published online January 31, 2012
Digital Object Identifier
http://dx.doi.org/10.1137/110823237

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