Numerical Solution of a Scalar One-Dimensional Monotonicity-Preserving Nonlocal Nonlinear Conservation Law
Received:December 05, 2016  Revised:December 19, 2016
Key Words: nonlocal model   nonlinear hyperbolic conservation laws   maximum principle   monotonicity preserving   numerical solution  
Fund Project:Supported in part by the NSF (Grant No.DMS-1558744), the AFOSR MURI Center for Material Failure Prediction Through Peridynamics and the ARO MURI (Grant No.W911NF-15-1-0562).
Author NameAffiliation
Qiang DU Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA 
Zhan HUANG Department of Mathematics, Penn State University, University Park, PA 16802, USA 
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Abstract:
      In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local conservation laws in the form of partial differential equations. We discuss convergent numerical approximations that preserve similar properties on the discrete level. We also present numerical experiments to study various limiting behavior of the numerical solutions.
Citation:
DOI:10.3770/j.issn:2095-2651.2017.01.001
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