TY - JOUR
T1 - Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations
AU - Liu , Yong
AU - Shu , Chi-Wang
AU - Zhang , Mengping
JO - Journal of Computational Mathematics
VL - 4
SP - 518
EP - 537
PY - 2021
DA - 2021/05
SN - 39
DO - http://doi.org/10.4208/jcm.2002-m2019-0305
UR - https://global-sci.org/intro/article_detail/jcm/19158.html
KW - Discontinuous Galerkin method, Central flux, Sub-optimal convergence rates.
AB - <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>