English

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 pp-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 pp 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}
}