scholarly journals Improved finite volume method for solving 1-D advection equation

2019 ◽  
Vol 1300 ◽  
pp. 012075
Author(s):  
Siyuan Zhao ◽  
Junjie Zhou ◽  
Chongbo Jing ◽  
Lingquan Li
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Advection Equation ◽  
Volume Method

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

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