We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the plate and the other one is supplied with the Dirichlet condition. The Neumann conditions are imposed on the whole remaining part of the boundary. Elements of the junction are assumed to have contrasting properties so that the small parameter, i.e. the relative thickness, appears in the differential equation, too, while the asymptotic structures crucially depend on the contrastness ratio. Asymptotic error estimates are derived in anisotropic weighted Sobolev norms.
@article{M2AN_2014__48_5_1495_0,
author = {Bunoiu, R. and Cardone, G. and Nazarov, S. A.},
title = {Scalar boundary value problems on junctions of thin rods and plates},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {48},
year = {2014},
pages = {1495-1528},
doi = {10.1051/m2an/2014007},
mrnumber = {3264363},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2014__48_5_1495_0}
}
Bunoiu, R.; Cardone, G.; Nazarov, S. A. Scalar boundary value problems on junctions of thin rods and plates. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014) pp. 1495-1528. doi : 10.1051/m2an/2014007. http://gdmltest.u-ga.fr/item/M2AN_2014__48_5_1495_0/
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