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math.NA2026
Runge--Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes
Manting Peng, Zhuoyun Li, Kailiang Wu
Nonlinear stabilization is indispensable for discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws, yet it typically disrupts the delicate error structure req…
math.NA2024
Spectral Volume from a DG perspective: Oscillation Elimination, Stability, and Optimal Error Estimates
Zhuoyun Li, Kailiang Wu
The discontinuous Galerkin (DG) method and the spectral volume (SV) method are two widely-used numerical methodologies for solving hyperbolic conservation laws. In this paper, we d…