We study a rather general class of 1D nonlocal conservation laws from a numerical point of view. First, following [F. Betancourt, R. Bürger, K.H. Karlsen and E.M. Tory, On nonlocal conservation laws modelling sedimentation. Nonlinearity 24 (2011) 855–885], we define an algorithm to numerically integrate them and prove its convergence. Then, we use this algorithm to investigate various analytical properties, obtaining evidence that usual properties of standard conservation laws fail in the nonlocal setting. Moreover, on the basis of our numerical integrations, we are led to conjecture the convergence of the nonlocal equation to the local ones, although no analytical results are, to our knowledge, available in this context.
Mots-clés : Nonlocal conservation laws, Lax Friedrichs scheme
@article{M2AN_2015__49_1_19_0,
author = {Amorim, Paulo and Colombo, Rinaldo M. and Teixeira, Andreia},
title = {On the {Numerical} {Integration} of {Scalar} {Nonlocal} {Conservation} {Laws}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {19--37},
publisher = {EDP-Sciences},
volume = {49},
number = {1},
year = {2015},
doi = {10.1051/m2an/2014023},
mrnumber = {3342191},
zbl = {1317.65165},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014023/}
}
TY - JOUR AU - Amorim, Paulo AU - Colombo, Rinaldo M. AU - Teixeira, Andreia TI - On the Numerical Integration of Scalar Nonlocal Conservation Laws JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 19 EP - 37 VL - 49 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014023/ DO - 10.1051/m2an/2014023 LA - en ID - M2AN_2015__49_1_19_0 ER -
%0 Journal Article %A Amorim, Paulo %A Colombo, Rinaldo M. %A Teixeira, Andreia %T On the Numerical Integration of Scalar Nonlocal Conservation Laws %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 19-37 %V 49 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014023/ %R 10.1051/m2an/2014023 %G en %F M2AN_2015__49_1_19_0
Amorim, Paulo; Colombo, Rinaldo M.; Teixeira, Andreia. On the Numerical Integration of Scalar Nonlocal Conservation Laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 1, pp. 19-37. doi : 10.1051/m2an/2014023. http://www.numdam.org/articles/10.1051/m2an/2014023/
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