Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs
Numerical Analysis
2018-05-07 v1
Abstract
In this paper we study numerical approximations of the evolution problem for the nonlocal -Laplacian operator with homogeneous Neumann boundary conditions on inhomogeneous random convergent graph sequences. More precisely, for networks on convergent inhomogeneous random graph sequences (generated first by deterministic and then random node sequences), we establish their continuum limits and provide rate of convergence of solutions for the discrete models to their continuum counterparts as the number of vertices grows. Our bounds reveals the role of the different parameters, and in particular that of and the geometry/regularity of the data.
Keywords
Cite
@article{arxiv.1805.01754,
title = {Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs},
author = {Yosra Hafiene and Jalal Fadini and Christophe Chesneau and Abderrahim Elmoataz},
journal= {arXiv preprint arXiv:1805.01754},
year = {2018}
}