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A Posteriori Error Estimates for Conservative Local Discontinuous GalerkinMethods for the Generalized Korteweg-de Vries Equation

Part of: Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  22 June 2016

Ohannes Karakashian  and
Yulong Xing
Ohannes Karakashian*
Affiliation:
Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, USA
Yulong Xing*
Affiliation:
Department of Mathematics, University of California Riverside, Riverside, CA 92521, USA
*
*Corresponding author. Email addresses:ohannes@math.utk.edu (O. Karakashian), xingy@ucr.edu (Y. Xing)
*Corresponding author. Email addresses:ohannes@math.utk.edu (O. Karakashian), xingy@ucr.edu (Y. Xing)
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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.

Keywords

Discontinuous Galerkin methodsKorteweg-de-Vries equationa posteriori error estimateconservative methods

MSC classification

Secondary: 65M12: Stability and convergence of numerical methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 35Q53: KdV-like equations (Korteweg-de Vries)
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 1 , July 2016 , pp. 250 - 278
Copyright
Copyright © Global-Science Press 2016 

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