In this paper we study numerical approximations of the evolution problem governed by the nonlocal p-Laplacian operator with a given kernel and homogeneous Neumann boundary conditions. More precisely, we consider discretized versions on inhomogeneous random graph sequences, establish their continuum limits and provide error bounds with nonasymptotic rate of convergence of solutions of the discrete problems to their continuum counterparts as the number of vertices grows. Our bounds reveal the role of the different parameters that come into play, and in particular that of p and of the geometry/regularity of the initial data and the kernel.
Mots-clés : Nonlocal diffusion, $$-Laplacian, inhomogeneous random graphs, graph limits, graphon, numerical approximation
@article{M2AN_2020__54_2_565_0,
author = {Hafiene, Yosra and Fadili, Jalal M. and Chesneau, Christophe and Elmoataz, Abderrahim},
title = {Continuum limit of the nonlocal $p${-Laplacian} evolution problem on random inhomogeneous graphs},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {565--589},
publisher = {EDP-Sciences},
volume = {54},
number = {2},
year = {2020},
doi = {10.1051/m2an/2019066},
mrnumber = {4068304},
zbl = {1442.65212},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2019066/}
}
TY - JOUR AU - Hafiene, Yosra AU - Fadili, Jalal M. AU - Chesneau, Christophe AU - Elmoataz, Abderrahim TI - Continuum limit of the nonlocal $p$-Laplacian evolution problem on random inhomogeneous graphs JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 565 EP - 589 VL - 54 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2019066/ DO - 10.1051/m2an/2019066 LA - en ID - M2AN_2020__54_2_565_0 ER -
%0 Journal Article %A Hafiene, Yosra %A Fadili, Jalal M. %A Chesneau, Christophe %A Elmoataz, Abderrahim %T Continuum limit of the nonlocal $p$-Laplacian evolution problem on random inhomogeneous graphs %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 565-589 %V 54 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2019066/ %R 10.1051/m2an/2019066 %G en %F M2AN_2020__54_2_565_0
Hafiene, Yosra; Fadili, Jalal M.; Chesneau, Christophe; Elmoataz, Abderrahim. Continuum limit of the nonlocal $p$-Laplacian evolution problem on random inhomogeneous graphs. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 2, pp. 565-589. doi : 10.1051/m2an/2019066. http://www.numdam.org/articles/10.1051/m2an/2019066/
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