A Posteriori Error Estimates for Conservative Local Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation (Communications in Computational Physics, 2018)
We construct and analyze conservative local discontinuous Galerkin (LDG)methods for the Generalized Korteweg-de-Vries equation. LDG methods are designedby writing the equation as a system and performing separate approximations to thespatial derivatives. The main focus is on the development of conservative methodswhich 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 onthe idea of dispersive reconstruction. Numerical experiments are provided to verifythe theoretical estimates.