## Preprint 2009-16

## Gabriel N. Gatica, George C. Hsiao, Francisco J. Sayas:

### Relaxing the hypotheses of the Bielak-MacCamy BEM-FEM coupling

### 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. 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 simplifed proof of the ellipticity of the Johnson-Nedelec 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.

This preprint gave rise to the following definitive publication(s):

**Gabriel N. GATICA, George C. HSIAO, Francisco J. SAYAS: ***Relaxing the hypotheses of the Bielak-MacCamy BEM-FEM coupling*. Numerische Mathematik, vol. 120, 3, pp. 465-487, (2012).