# CONFLUENTES MATHEMATICI

Approximation of the two-dimensional Dirichlet problem by continuous and discrete problems on one-dimensional networks
Confluentes Mathematici, Tome 7 (2015) no. 1, pp. 13-33.

We show that the solution of the two-dimensional Dirichlet problem set in a plane domain is the limit of the solutions of similar problems set on a sequence of one-dimensional networks as their size goes to zero. Roughly speaking this means that a membrane can be seen as the limit of rackets made of strings. For practical applications, we also show that the solutions of the discrete approximated problems (again on the one-dimensional networks) also converge to the solution of the two-dimensional Dirichlet problem.

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DOI : https://doi.org/10.5802/cml.16
Classification : 35R02,  35B40,  65N30
@article{CML_2015__7_1_13_0,
author = {Maryse Bourlard-Jospin and Serge Nicaise and Juliette Venel},
title = {Approximation of the two-dimensional {Dirichlet} problem by continuous and discrete problems on one-dimensional networks},
journal = {Confluentes Mathematici},
pages = {13--33},
publisher = {Institut Camille Jordan},
volume = {7},
number = {1},
year = {2015},
doi = {10.5802/cml.16},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.16/}
}
Maryse Bourlard-Jospin; Serge Nicaise; Juliette Venel. Approximation of the two-dimensional Dirichlet problem by continuous and discrete problems on one-dimensional networks. Confluentes Mathematici, Tome 7 (2015) no. 1, pp. 13-33. doi : 10.5802/cml.16. https://cml.centre-mersenne.org/articles/10.5802/cml.16/

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