Numerical smoothness and error analysis for RKDG on the scalar nonlinear conservation laws

Authors:
Tong Sun;David Rumsey
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 4
Cited 0

Finite difference schemes and partial differential equations

Finite difference schemes and partial differential equations
Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws

SIAM Journal on Numerical Analysis
Long-time error estimation for semi-linear parabolic equations

Journal of Computational and Applied Mathematics
Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge-Kutta Discontinuous Galerkin Method for Scalar Conservation Laws

SIAM Journal on Numerical Analysis

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Abstract

The new concept of numerical smoothness is applied to the RKDG (Runge-Kutta/Discontinuous Galerkin) methods for scalar nonlinear conservations laws. The main result is an a posteriori error estimate for the RKDG methods of arbitrary order in space and time, with optimal convergence rate. In this paper, the case of smooth solutions is the focus point. However, the error propagation analysis framework is prepared to deal with discontinuous solutions in the future.