On the stability of the non-symmetric BEM/FEM coupling in linear elasticity
Computational Mechanics
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We describe a mixed boundary element discretization of the Steklov--Poincaré operator related to a three-dimensional boundary value problem with mixed boundary conditions of Dirichlet and Neumann type. The Galerkin discretization of the Steklov--Poincaré operator is replaced by a mixed approximation based on a boundary integral equation including single and double layer potentials only, where appropriate stability conditions have to be assumed. We show that the required stability conditions hold when either isoparametric trial functions are used or when the approximation of the Steklov--Poincaré operator is done on a refined boundary element mesh. A numerical example for a mixed boundary value problem for the Laplace equation confirms the theoretical results.