A least-squares fem-bem coupling method for linear elasticity

This paper deals with a least-squares formulation of a second order transmission problem for linear elasticity. The problem in the unbounded exterior domain is rewritten with boundary integral equations on the boundary of the inner domain. In the interior domain we treat a linear elastic material which can also be nearly incompressible. The least-squares functional is given in terms of the H ˜ − 1 ( Ω ) and H 1 / 2 ( Γ ) norms. These norms are realized by solution operators of corresponding dual norm problems which are approximated using multilevel preconditioners.