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math.NA2024★ 1 cited
The Runge--Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws
Qifan Chen, Zheng Sun, Yulong Xing
In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the trad…
math.NA2023★ 2 cited
The Runge--Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws
Qifan Chen, Zheng Sun, Yulong Xing
In this paper, we develop a new type of Runge--Kutta (RK) discontinuous Galerkin (DG) method for solving hyperbolic conservation laws. Compared with the original RKDG method, the n…