@article{ref1,
title="A finite element approach for the traffic assignment problem",
journal="Transportation research procedia",
year="2021",
author="Cortínez, Víctor H. and Dominguez, Patricia N.",
volume="58",
number="",
pages="13-20",
abstract="In this article, a reduced order model for the Transportation Assignment Problem (TAP), based on a Finite Element Approach (FEA), is proposed. Such methodology involves four main ideas: a) the TAP formulation including, as variables, the travel times from any node of the network to the corresponding destination points; b) the solution of the governing algebraic equation system by means of an efficient iterative approach, known as &quot;Physarum&quot;, that takes the travel times as the main unknowns; c) the interpolation of travel times in certain urban subdomains, denominated &quot;finite elements&quot;, in terms of the values corresponding to some main nodes previously selected (reduced unknowns); d) the use of the Galerkin's method to express the TAP in terms of the reduced unknowns. The model formulation is presented and a numerical example is given to show its efficiency.<p /> <p>Language: en</p>",
language="en",
issn="2352-1465",
doi="10.1016/j.trpro.2021.11.003",
url="http://dx.doi.org/10.1016/j.trpro.2021.11.003"
}