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.

Reçu le : 2014-10-19
Révisé le : 2015-02-18
Accepté le : 2015-02-18
Publié le : 2016-02-03
Classification : 35R02,  35B40,  65N30
     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},
     publisher = {Institut Camille Jordan},
     volume = {7},
     number = {1},
     year = {2015},
     pages = {13-33},
     doi = {10.5802/cml.16},
     language = {en},
     url = {}
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.

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