| Issue |
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
|
|
|---|---|---|
| Page(s) | 1401 - 1435 | |
| DOI | https://doi.org/10.1051/m2an/2022037 | |
| Published online | 27 June 2022 | |
Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws*
1
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
2
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
* Corresponding author: jmj123@mail.ustc.edu.cn
Received:
2
July
2021
Accepted:
12
April
2022
In this paper, we study the error estimates to sufficiently smooth solutions of the nonlinear scalar conservation laws for the semi-discrete central discontinuous Galerkin (DG) finite element methods on uniform Cartesian meshes. A general approach with an explicitly checkable condition is established for the proof of optimal L2 error estimates of the semi-discrete CDG schemes, and this condition is checked to be valid in one and two dimensions for polynomials of degree up to k = 8. Numerical experiments are given to verify the theoretical results.
Mathematics Subject Classification: 65M12 / 65M15 / 65M60
Key words: Central DG method / nonlinear conservation laws / optimal error estimates
Supplementary Online Material is only available in electronic form at https://doi.org/10.1051/m2an/2022037/olm.
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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