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Issue ESAIM: Proc.
Volume 21, 2007
Journées d'analyse fonctionnelle et numérique en l'honneur de Michel Crouzeix
Page(s) 88 - 97
DOI http://dx.doi.org/10.1051/proc:072107
Published online 04 December 2007

ESAIM: Proc., 2007, Vol. 21, pp. 88-97
DOI: 10.1051/proc:072107

A look at how LDG and BEM can be coupled

Rommel A. Bustinza1, Gabriel N. Gatica1 and Francisco-Javier Sayas2

1  GIMA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
2  Departamento de Matemática Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain


(September 2006 / Published online: 4 December 2007)

Abstract
In this work we explain the coupling of Local Discontinuous Galerkin and general Boundary Element methods for a class of nonlinear exterior transmission problems. The method is exposed as the discrete coupling of two Neumann-to-Dirichlet operators, one coping with all nonlinearities and source terms and the other for a purely exterior Laplace equation. We show how two separate methods for interior and exterior problems can be coupled at a weak level using a mortar space and how the analysis can be organised with very little interaction of the interior and exterior parts by considering the natural seminorms to measure the influence of the coupling unknown on the different methods.


Mathematics Subject Classification. 65N30, 65N38

Key words: Boundary elements, Local Discontinuous Galerkin, coupling, nonlinear problems


© EDP Sciences, ESAIM 2007


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