A Posteriori Error Estimates for Conservative Local Discontinuous GalerkinMethods for the Generalized Korteweg-de Vries Equation. (22nd June 2016)

• Record Type: Journal Article
• Authors: Karakashian, Ohannes; Xing, Yulong
• Is Part Of: Communications in computational physics. Volume 20:Number 1(2016:Jul.)
• Page Start: 250
• Page End: 278
• Publication Date: 2016-06-22
• Subjects: 65M12, -- 65M60, -- 35Q53; Discontinuous Galerkin methods, -- Korteweg-de-Vries equation, -- a posteriori error estimate, -- conservative methods; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.240815.301215a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: We construct and analyze conservative local discontinuous Galerkin (LDG) methods for the Generalized Korteweg-de-Vries equation. LDG methods are designed by writing the equation as a system and performing separate approximations to the spatial derivatives. The main focus is on the development of conservative methods which can preserve discrete versions of the first two invariants of the continuous solution, and a posteriori error estimates for a fully discrete approximation that is based on the idea of dispersive reconstruction. Numerical experiments are provided to verify the theoretical estimates.