A fully discrete BEM–FEM method for an exterior elasticity system in the plane

We present a modified version of the usual BEM–FEM coupling for the exterior elasticity problem in the plane (cf. Costabel and Stephan, SIAM J. Numer. Anal. 27 (1990) 1212–1226). This new formulation allows us to take advantage of techniques from Hsiao et al., Computing 25 (1980) 557–566 to compute the boundary integral terms using simple quadrature formulas. We provide error estimates for the Galerkin method and prove that the corresponding fully discrete scheme preserves the optimal rates of convergence.