Qiang DU,Zhan HUANG.Numerical Solution of a Scalar One-Dimensional Monotonicity-Preserving Nonlocal Nonlinear Conservation Law[J].数学研究及应用,2017,37(1):1~18
Numerical Solution of a Scalar One-Dimensional Monotonicity-Preserving Nonlocal Nonlinear Conservation Law
Numerical Solution of a Scalar One-Dimensional Monotonicity-Preserving Nonlocal Nonlinear Conservation Law
投稿时间:2016-12-05  最后修改时间:2016-12-19
DOI:10.3770/j.issn:2095-2651.2017.01.001
中文关键词:  nonlocal model  nonlinear hyperbolic conservation laws  maximum principle  monotonicity preserving  numerical solution
英文关键词:nonlocal model  nonlinear hyperbolic conservation laws  maximum principle  monotonicity preserving  numerical solution
基金项目: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).
作者单位
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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中文摘要:
      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.
英文摘要:
      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.
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