A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws. (9th November 2018)

• Record Type: Journal Article
• Authors: Chatterjee, N; Fjordholm, U S
• Is Part Of: IMA journal of numerical analysis. Volume 40:Number 1(2020)
• Page Start: 405
• Page End: 421
• Publication Date: 2018-11-09
• Subjects: nonlocal conservation laws -- finite volume methods -- Kuramoto equation; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry074
• Languages: English
• ISSNs: 0272-4979

Abstract

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.