2.1 Review of the RKDG method on unstructured mesh

We show that while Runge-Kutta methods cannot preserve polynomial invariants in gen- eral, they can preserve polynomials that are the energy invariant of canonical Hamiltonian

Abstract — In this work we introducé and analyze the model scheme of a new class of methods devised for numencally solving hyperbohc conservation laws The construction of the scheme

The difference between the conservative and dissipative scheme only exits in the choices of numerical flux f which is reflected in the term H j , yet the same estimate results for H

We study semi-Lagrangian discontinuous Galerkin (SLDG) and Runge- Kutta discontinuous Galerkin (RKDG) schemes for some front propagation prob- lems in the presence of an obstacle

The general framework of such HWENO limiters for RKDG methods, namely first identifying troubled cells subject to the HWENO limiting, then reconstruct- ing the polynomial

In this paper we would like to continue the works in [29–31] and present error estimates of the Runge-Kutta discontinuous Galerkin (RKDG) method for smooth solutions of

In this paper, we adapt a simple weighted essentially non-oscillatory (WENO) lim- iter, originally designed for discontinuous Galerkin (DG) schemes on two-dimensional un-

Shu, Stability analysis and a priori error estimate to the third order explicit Runge-Kutta discontinuous Galerkin method for scalar conservation laws, SIAM Journal on