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ERROR ESTIMATE OF THE FOURTH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN METHODS FOR LINEAR HYPERBOLIC EQUATIONS.
- Source :
- SIAM Journal on Numerical Analysis; 2020, Vol. 58 Issue 5, p2885-2914, 30p
- Publication Year :
- 2020
-
Abstract
- In this paper we consider the Runge-Kutta discontinuous Galerkin (RKDG) method to solve linear constant-coefficient hyperbolic equations, where the fourth-order explicit Runge- Kutta time-marching is used. By the aid of the equivalent evolution representation with temporal differences of stage solutions, we make a detailed investigation on the matrix transferring process about the energy equations and then present a sufficient condition to ensure the L²-norm stability under the standard Courant-Friedrichs-Lewy condition. If the source term is equal to zero, we achieve the strong (boundedness) stability without the matrix transferring process to multiple-steps time-marching of the RKDG method. By carefully introducing the reference functions and their projections, we obtain the optimal (or suboptimal) error estimate under a mild smoothness assumption on the exact solution, which is independent of the stage number of the RKDG method. Some numerical experiments are also given to verify our conclusions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 58
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 147633645
- Full Text :
- https://doi.org/10.1137/19M1280077