A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes

2010 ◽  
Vol 31 (6) ◽  
pp. 4066-4099 ◽  
Author(s):  
Donna A. Calhoun ◽  
Christiane Helzel
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Parabolic Equations ◽  
Curved Surface ◽  
Surface Meshes ◽  
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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