451. Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs
- Author
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Jalal M. Fadili, Christophe Chesneau, Abderrahim Elmoataz, Yosra Hafiene, Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Normandie Université (NU)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU), École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Université de Caen Normandie (UNICAEN), and Fadili, Jalal
- Subjects
[INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing ,02 engineering and technology ,[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] ,01 natural sciences ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,[STAT.ML]Statistics [stat]/Machine Learning [stat.ML] ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,0202 electrical engineering, electronic engineering, information engineering ,Neumann boundary condition ,FOS: Mathematics ,Mathematics - Numerical Analysis ,Limit (mathematics) ,0101 mathematics ,graph limits ,[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST] ,Mathematics ,Random graph ,Numerical Analysis ,[STAT.TH] Statistics [stat]/Statistics Theory [stat.TH] ,Continuum (topology) ,Applied Mathematics ,Operator (physics) ,Nonlocal diffusion ,Mathematical analysis ,p-Laplacian ,[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA] ,[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC] ,020206 networking & telecommunications ,Numerical Analysis (math.NA) ,[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] ,[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] ,[STAT.ML] Statistics [stat]/Machine Learning [stat.ML] ,010101 applied mathematics ,Computational Mathematics ,Rate of convergence ,[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] ,Modeling and Simulation ,inhomogeneous random graphs ,Node (circuits) ,[INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT] ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Analysis ,numerical approximation ,[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] - Abstract
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.
- Published
- 2019