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

A Posteriori Error Estimates for Conservative Local Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation
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Year:    2016

Communications in Computational Physics, Vol. 20 (2016), Iss. 1 : pp. 250–278

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.240815.301215a

Communications in Computational Physics, Vol. 20 (2016), Iss. 1 : pp. 250–278

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:   

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