Open Access
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 |
- Y. Cheng and C.-W. Shu, A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives. Math. Comput. 77 (2008) 699–730. [Google Scholar]
- P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North Holland Publishing Company (1978). [Google Scholar]
- A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations. J. Comput. Phys. 160 (2000) 241–282. [NASA ADS] [CrossRef] [Google Scholar]
- R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge University Press (2002). [CrossRef] [Google Scholar]
- F. Li and L. Xu, Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations. J. Comput. Phys. 231 (2012) 2655–2675. [CrossRef] [MathSciNet] [Google Scholar]
- F. Li, L. Xu and S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field. J. Comput. Phys. 230 (2011) 4828–4847. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Liu, Central schemes and central discontinuous Galerkin methods on overlapping cells. In: Conference on Analysis, Modeling and Computation of PDE and Multiphase Flow. Stony Brook, NY (2004). [Google Scholar]
- Y. Liu, Central schemes on overlapping cells. J. Comput. Phys. 209 (2005) 82–104. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang, Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction. SIAM J. Numer. Anal. 45 (2007) 2442–2467. [Google Scholar]
- Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang, L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods. ESAIM: M2AN 42 (2008) 593–607. [CrossRef] [EDP Sciences] [Google Scholar]
- Y. Liu, C.-W. Shu, E. Tadmor and M. Zhang, Central local discontinuous Galerkin methods on overlapping cells for diffusion equations. ESAIM: M2AN 45 (2011) 1009–1032. [CrossRef] [EDP Sciences] [Google Scholar]
- Y. Liu, C.-W. Shu and M. Zhang, Optimal Error estimates of the semidiscrete central discontinuous Galerkin methods for linear hyperbolic equations. SIAM J. Numer. Anal. 56 (2018) 520–541. [CrossRef] [MathSciNet] [Google Scholar]
- J. Luo, C.-W. Shu and Q. Zhang, A priori error estimates to smooth solutions of the third order Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws. ESAIM: M2AN 49 (2015) 991–1018. [CrossRef] [EDP Sciences] [Google Scholar]
- H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [CrossRef] [MathSciNet] [Google Scholar]
- M.A. Reyna and F. Li, Operator bounds and time step conditions for DG and central DG methods. J. Sci. Comput. 62 (2015) 532–554. [Google Scholar]
- Z. Xu and Y. Liu, New central and central discontinuous Galerkin schemes on overlapping cells of unstructured grids for solving ideal magnetohydrodynamic equations with globally divergence-free magnetic field. J. Comput. Phys. 327 (2016) 203–224. [Google Scholar]
- Y. Xu and C.-W. Shu, Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection–diffusion and KdV equations. Comput. Methods Appl. Mech. Eng. 196 (2007) 3805–3822. [CrossRef] [Google Scholar]
- S. Yakovlev, L. Xu and F. Li, Locally divergence-free central discontinuous Galerkin methods for ideal MHD equations. J. Comput. Sci. 4 (2013) 80–91. [CrossRef] [Google Scholar]
- Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. SIAM J. Numer. Anal. 42 (2004) 641–666. [Google Scholar]
- Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws. SIAM J. Numer. Anal. 44 (2006) 1703–1720. [CrossRef] [MathSciNet] [Google Scholar]
- Q. Zhang and C.-W. Shu, Stability analysis and a priori error estimates of the third order explicit Runge-Kutta discontinuous Galerkin method for scalar conservation laws. SIAM J. Numer. Anal. 48 (2010) 1038–1063. [CrossRef] [MathSciNet] [Google Scholar]
- J. Zhao and H. Tang, Runge-Kutta central discontinuous Galerkin methods for the special relativistic hydrodynamics. Commun. Comput. Phys. 22 (2017) 643–682. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.