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@article{faucris.110144804,
abstract = {We consider elliptic problems on graphs under given loads and bilateral contact conditions. We ask the question: which graph is best suited to sustain the loads and the constraints. More precisely, given a cost function we may look at a multiple node of the graph with edge degree q and ask as to whether that node should be resolved into a number of nodes of edge degree less than q, in order to decrease the cost. With this question in mind, we are looking into the sensitivity analysis of a graph carrying a second order elliptic equation with respect to changing its topology by releasing nodes with high edge degree or including an edge. With the machinery at hand developed here, we are in the position to define the topological gradient of an elliptic problem on a graph.},
author = {Leugering, Günter and Sokolowski, Jan},
faupublication = {yes},
journal = {Control and Cybernetics},
keywords = {differential equations on metric graphs;obstacles;topology optimization;asymptotic analysis},
month = {Jan},
pages = {971-997},
peerreviewed = {Yes},
title = {{Topological} sensitivity analysis for elliptic problems on graphs},
url = {https://hal.archives-ouvertes.fr/hal-00261861/},
volume = {37},
year = {2008}
}