### Luka Grubišić, Josip Iveković, Josip Tambača and Bojan Žugec

Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: luka.grubisic@math.hr

Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: jivekovi@gmail.com

Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: tambaca@math.hr

Faculty of Organization and Informatics, University of Zagreb, 42 000 Varaždin, Croatia
e-mail: bojan.zugec@foi.hr

Abstract.   In this paper we formulate and analyze the mixed formulation of the one-dimensional equilibrium model of elastic stents. The model is based on the curved rod model for the inextensible and ushearable struts and is formulated in the weak form in [5]. It is given by a system of ordinary differential equations at the graph structure. In order to numerically treat the model using finite element method the mixed formulation is plead for. We obtain equivalence of the weak and the mixed formulation by proving the Babuska–Brezzi (inf-sup) condition for the stent structure.

2010 Mathematics Subject Classification.   74K10, 74K30, 74B05.

Key words and phrases.   Stents, one-dimensional model, curved rod model, mixed formulation, inf-sup condition.

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