@Article{JCM-39-518,
author = {Liu , YongShu , Chi-Wang and Zhang , Mengping},
title = {Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations},
journal = {Journal of Computational Mathematics},
year = {2021},
volume = {39},
number = {4},
pages = {518--537},
abstract = {<p style="text-align: justify;">In this paper, we theoretically and numerically verify that the discontinuous Galerkin
(DG) methods with central fluxes for linear hyperbolic equations on non-uniform meshes
have sub-optimal convergence properties when measured in the $L^2$-norm for even degree
polynomial approximations. On uniform meshes, the optimal error estimates are provided
for arbitrary number of cells in one and multi-dimensions, improving previous results. The
theoretical findings are found to be sharp and consistent with numerical results.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2002-m2019-0305},
url = {http://global-sci.org/intro/article_detail/jcm/19158.html}
}