  This paper deals with the analysis of a coupled problem arising from linear
magneto-elastostaticity. The model, which can be derived by an energy
principle, gives valuable insight into the coupling mechanism and features a
saddle point structure with the elastic displacement and magnetic scalar
potential as independent variables. As main results, the existence and
uniqueness of the solution are proven for the continuous and discrete cases and
special properties of the corresponding bilinear forms are shown. In
particular, the coupled magneto-elastic bilinear form satisfies an inf-sup
condition that is essential for the stability of the problem.
