Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 27, 2022
- Source ID
- 10.1051/m2an/2022037
Entities
People
- Chi-Wang Shu
- Mengjiao Jiao
- Mengping Zhang
- Yan Jiang
Organizations
- Air Force Office of Scientific Research
- National Natural Science Foundation of China
- National Science Foundation