On a saddle point problem arising from magneto-elastic coupling

TL;DR

This paper analyzes a coupled magneto-elastostatic problem with a saddle point structure, proving existence, uniqueness, and stability of solutions for both continuous and discrete models, providing insights into the coupling mechanism.

Contribution

It establishes the existence, uniqueness, and stability of solutions for a magneto-elastostatic saddle point problem, including properties of the bilinear forms involved.

Findings

Proven existence and uniqueness of solutions.

Demonstrated inf-sup stability condition.

Analyzed properties of the coupled bilinear form.

Abstract

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.