Direct solution method for the equilibrium problem for elastic stents

We are interested in numerical methods for approximating vector‐valued functions on a metric graph. As a model problem, we formulate and analyze a numerical method for the solution of the stationary problem for the one‐dimensional elastic stent model. The approximation is built using the mixed finite element method. The discretization matrix is a symmetric saddle‐point matrix, and we discuss sparse direct methods for the fast and robust solution of the associated equilibrium system. The convergence of the numerical method is proven and the error estimate is obtained. Numerical examples confirm the theoretical estimates.