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On the stability of the non-symmetric BEM/FEM coupling in linear elasticity

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Abstract

In this paper we discuss the use of single and double layer boundary integral equations for the numerical solution of linear elasticity problems with boundary conditions of mixed type, and the one-equation coupling of finite and boundary element methods to solve a free space transmission problem. In particular we present a sufficient and necessary condition which ensures stability of the coupled approach for any choice of finite and boundary elements. These results justify the coupling of collocation and Galerkin one-equation boundary element methods with finite elements as used in many engineering and industrial applications. Hence one may avoid the use of the symmetric formulation of boundary integral equations, which is, although well established from a mathematical point of view and also used in some engineering applications, not so much accepted in particular in industrial applications.

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  1. Institut für Numerische Mathematik, TU Graz, Steyrergasse 30, 8010, Graz, Austria

    Olaf Steinbach

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  1. Olaf Steinbach
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Steinbach, O. On the stability of the non-symmetric BEM/FEM coupling in linear elasticity. Comput Mech 51, 421–430 (2013). https://doi.org/10.1007/s00466-012-0782-y

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  • DOI: https://doi.org/10.1007/s00466-012-0782-y

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