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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.
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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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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, Institut Camille Jordan et Unité de Mathématiques Pures et Appliquées, 2015, 7 (1), pp.13-33. ⟨10.5802/cml.16⟩. ⟨hal-03135676⟩

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