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math.NA2026
A Local Discontinuous Galerkin method for the modified Camassa--Holm equation
Xiang-Ke Chang, Yong Liu, Qi Tao
In this paper, we propose a local discontinuous Galerkin (LDG) method for the modified Camassa-Holm (mCH) equation that contains cubic nonlinearity and high-order derivative terms.…
math.NA2026
The error estimate of entropy-stable discontinuous Galerkin methods for hyperbolic conservation laws
Xu-Kun Chen, Yong Liu, Chi-Wang Shu
Entropy inequalities are fundamental to the well-posedness of hyperbolic conservation laws, providing the essential criterion for selecting the physically admissible solution among…
math.NA2026
Weighted Inverse Lax-Wendroff Boundary Treatment of Discontinuous Galerkin Methods for Conservation Laws
Yongjie Bi, Yan Jiang, Yong Liu
In this paper, we propose a weighted inverse Lax-Wendroff (WILW) boundary treatment for the discontinuous Galerkin (DG) method on unfitted meshes to efficiently solve hyperbolic co…