Year: 2020
Author: Mengjiao Jiao, Yingda Cheng, Yong Liu, Mengping Zhang
Communications in Computational Physics, Vol. 28 (2020), Iss. 3 : pp. 927–966
Abstract
In this paper, we develop central discontinuous Galerkin (CDG) finite element methods for solving the generalized Korteweg-de Vries (KdV) equations in one dimension. Unlike traditional discontinuous Galerkin (DG) method, the CDG methods evolve two approximate solutions defined on overlapping cells and thus do not need numerical fluxes on the cell interfaces. Several CDG schemes are constructed, including the dissipative and non-dissipative versions. L2 error estimates are established for the linear and nonlinear equation using several projections for different parameter choices. Although we can not provide optimal a priori error estimate, numerical examples show that our scheme attains the optimal (k+1)-th order of accuracy when using piecewise k-th degree polynomials for many cases.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0099
Communications in Computational Physics, Vol. 28 (2020), Iss. 3 : pp. 927–966
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Korteweg-de Vries equation central DG method stability error estimates.