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Journal articles
Approximation of the two-dimensional Dirichlet problem by continuous and discrete problems on one-dimensional networks
Abstract : 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.
https://hal-uphf.archives-ouvertes.fr/hal-03135676
Contributor : Julie Cagniard Connect in order to contact the contributor
Submitted on : Tuesday, February 9, 2021 - 10:47:49 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM
Contributor : Julie Cagniard Connect in order to contact the contributor
Submitted on : Tuesday, February 9, 2021 - 10:47:49 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM
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