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.
Domaines
Analyse numérique [math.NA]
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Approximation_on_a_network_of_the_Dirichlet_problem_hal.pdf (648.52 Ko)
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