On a saddle point problem arising from magneto-elastic coupling

This paper deals with the analysis of a coupled problem arising from linear magneto-elastostatics. 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 for a certain class of magnetostrictive materials, that is essential for the stability of the problem.