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Direct solution method for the equilibrium problem for elastic stents
Author(s) -
Grubišić Luka,
Tambača Josip
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2231
Subject(s) - discretization , mathematics , saddle point , numerical analysis , finite element method , convergence (economics) , matrix (chemical analysis) , saddle , mathematical optimization , mathematical analysis , geometry , physics , materials science , economics , composite material , thermodynamics , economic growth
Summary 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.