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Pré-Publication, Document De Travail Année : 2013

Approximation of the two-dimensional Dirichlet problem by one-dimensional continuous and discrete problems on one-dimensional networks

Résumé

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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Dates et versions

hal-00834307 , version 1 (18-06-2013)

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  • HAL Id : hal-00834307 , version 1

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Maryse Bourlard-Jospin, Serge Nicaise, Juliette Venel. Approximation of the two-dimensional Dirichlet problem by one-dimensional continuous and discrete problems on one-dimensional networks. 2013. ⟨hal-00834307⟩
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