Relaxing the hypotheses of Bielak–MacCamy’s BEM–FEM coupling |
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Authors: | Gabriel N Gatica George C Hsiao Francisco-Javier Sayas |
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Institution: | 1. Centro de Investigación en Ingeniería Matemática (CI2MA) and Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile 2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19176-2553, USA
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Abstract: | In this paper we show that the quasi-symmetric coupling of finite and boundary elements of Bielak and MacCamy can be freed
of two very restricting hypotheses that appeared in the original paper: the coupling boundary can be taken polygonal/polyhedral
and coupling can be done using the normal stress instead of the pseudostress. We will do this by first considering a model
problem associated to the Yukawa equation, where we prove how compactness arguments can be avoided to show stability of Galerkin
discretizations of a coupled system in the style of Bielak–MacCamy’s. We also show how discretization properties are robust
in the continuation parameter that appears in the formulation. This analysis is carried out using a new and very simplified
proof of the ellipticity of the Johnson–Nédélec BEM–FEM coupling operator. Finally, we show how to apply the techniques that
we have fully developed in the model problem to the linear elasticity system. |
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