Calculus of Variations and Geometric Measure Theory
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M. Bonnivard - E. Bretin - A. Lemenant

Numerical approximation of the Steiner problem in dimension 2 and 3

created by lemenant on 04 Dec 2019


Accepted Paper

Inserted: 4 dec 2019
Last Updated: 4 dec 2019

Journal: Mathematics of computation
Year: 2020

preprint april 2018


The aim of this work is to present some numerical computations of solutions of the Steiner Prob- lem, based on the recent phase field approximations proposed in 12 and analyzed in 5, 4. Our strategy consists in improving the regularity of the associated phase field solution by use of higher- order derivatives in the Cahn-Hilliard functional as in 6. We justify the convergence of this slightly modified version of the functional, together with other technics that we employ to improve the nu- merical experiments. In particular, we are able to consider a large number of points in dimension 2. We finally present and justify an approximation method that is efficient in dimension 3, which is one of the major novelties of the paper.


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