Approximation of the two-dimensional Dirichlet problem by continuous and discrete problems on one-dimensional networks
Bourlard-Jospin, Maryse ; Nicaise, Serge ; Venel, Juliette
Confluentes Mathematici, Tome 7 (2015), p. 13-33 / Harvested from Numdam
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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.

Publié le : 2015-01-01
DOI : https://doi.org/10.5802/cml.16
Classification:  35R02,  35B40,  65N30 
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     title = {Approximation of the two-dimensional Dirichlet problem by continuous and discrete problems on one-dimensional networks},
     journal = {Confluentes Mathematici},
     volume = {7},
     year = {2015},
     pages = {13-33},
     doi = {10.5802/cml.16},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CML_2015__7_1_13_0}
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Bourlard-Jospin, Maryse; Nicaise, Serge; Venel, Juliette. Approximation of the two-dimensional Dirichlet problem by continuous and discrete problems on one-dimensional networks. Confluentes Mathematici, Tome 7 (2015) pp. 13-33. doi : 10.5802/cml.16. http://gdmltest.u-ga.fr/item/CML_2015__7_1_13_0/

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