The Validity of Johnson-Nédélec's BEM-FEM Coupling on Polygonal Interfaces
SIAM Journal on Numerical Analysis
Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
Computational Mechanics
On the stability of the non-symmetric BEM/FEM coupling in linear elasticity
Computational Mechanics
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In a recent paper [SIAM J. Numer. Anal., 47 (2009), pp. 3451-3463] Sayas proved the stability of the Johnson-Nédélec coupling of finite and boundary element methods on polygonal interfaces when the direct boundary integral equation with single and double layer integral operators is used only. In this note we present two alternative proofs of this result for general Lipschitz interfaces. In particular, we prove an ellipticity estimate of the coupled bilinear form. Hence, we can use standard arguments to derive stability and error estimates for the Galerkin discretization for all pairs of finite and boundary element trial spaces.