Volume 54, Number 2, March-April 2020
|Page(s)||565 - 589|
|Published online||25 February 2020|
Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs
Normandie Univ, ENSICAEN, UNICAEN, CNRS, GREYC, Caen, France
2 Normandie Univ, ENSICAEN, CNRS, GREYC, Caen, France
3 Normandie Univ, UNICAEN, CNRS, LMNO, Caen, France
4 Normandie Univ, UNICAEN, CNRS, GREYC, Caen, France
* Corresponding author: Jalal.Fadili@greyc.ensicaen.fr
Accepted: 31 August 2019
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.
Mathematics Subject Classification: 35A35 / 65N12 / 65N15 / 41A17 / 05C80
Key words: Nonlocal diffusion / p-Laplacian / inhomogeneous random graphs / graph limits / graphon / numerical approximation
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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