The present work is a continuation of a paper presented by the two first authors in the proceedings of the “Computational Science for the century” conference held in Tours in 1997 honouring the birthday of Roland Glowinski. It is devoted to the solution of 1D convection-diffusion equations in dominant convection regime situations. In that paper, an “a posteriori” VMS filtering technique was introduced. We present an extension of this technique to nonlinear convection-diffusion equations (a traffic model), providing an efficient method for the resolution of shocks from just the Galerkin solution at targeted times. We also present a residual-based “a posteriori” VMS filtering, that provides quite accurate stable solutions, can be extended to multi-dimensional problems, and can be applied locally. We finally present some numerical tests exhibiting the high accuracy of the obtained solutions.
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Tomás Chacón Rebollo 1; Antonio Domínguez-Delgado 2; Macarena Gómez Marmol 3
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@article{CRMECA_2023__351_S1_293_0,
author = {Tom\'as Chac\'on Rebollo and Antonio Dom{\'\i}nguez-Delgado and Macarena G\'omez Marmol},
title = {A posteriori {Variational} {Multiscale} {Methods} for the {1D} convection-diffusion equations},
journal = {Comptes Rendus. M\'ecanique},
pages = {293--305},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
number = {S1},
year = {2023},
doi = {10.5802/crmeca.187},
language = {en},
}
TY - JOUR AU - Tomás Chacón Rebollo AU - Antonio Domínguez-Delgado AU - Macarena Gómez Marmol TI - A posteriori Variational Multiscale Methods for the 1D convection-diffusion equations JO - Comptes Rendus. Mécanique PY - 2023 SP - 293 EP - 305 VL - 351 IS - S1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.187 LA - en ID - CRMECA_2023__351_S1_293_0 ER -
%0 Journal Article %A Tomás Chacón Rebollo %A Antonio Domínguez-Delgado %A Macarena Gómez Marmol %T A posteriori Variational Multiscale Methods for the 1D convection-diffusion equations %J Comptes Rendus. Mécanique %D 2023 %P 293-305 %V 351 %N S1 %I Académie des sciences, Paris %R 10.5802/crmeca.187 %G en %F CRMECA_2023__351_S1_293_0
Tomás Chacón Rebollo; Antonio Domínguez-Delgado; Macarena Gómez Marmol. A posteriori Variational Multiscale Methods for the 1D convection-diffusion equations. Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023) no. S1, pp. 293-305. doi : 10.5802/crmeca.187. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.187/
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