@Article{JCM-39-4,
author = {Yong, Liu and Shu, 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 = {https://global-sci.com/article/84248/sub-optimal-convergence-of-discontinuous-galerkin-methods-with-central-fluxes-for-linear-hyperbolic-equations-with-even-degree-polynomial-approximations}
}