# Mixed formulation of the one-dimensional equilibrium model for elastic stents

## TL;DR

This paper develops and analyzes a mixed finite element formulation for a one-dimensional elastic stent model based on curved rod theory, ensuring numerical stability and equivalence with the weak form.

## Contribution

It introduces a mixed formulation for the elastic stent model and proves its equivalence to the weak form via Babuska--Brezzi condition, facilitating numerical methods.

## Key findings

- Established equivalence of weak and mixed formulations.
- Proved Babuska--Brezzi condition for the stent model.
- Facilitated finite element numerical treatment.

## 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 \v{C}ani\'{c} and Tamba\v{c}a, 2012. 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 condition for the stent structure.