Runge-Kutta-Aligned Oscillation Elimination: Restoring Superconvergence for Fully Discrete Shock-Capturing DG Schemes

This paper addresses a critical gap in discontinuous Galerkin methods for hyperbolic conservation laws: nonlinear stabilization techniques typically destroy the delicate error structure required for superconvergence analysis. The authors propose a Runge-Kutta aligned oscillation-eliminating (OE) DG framework that restores the theoretical error structure while maintaining effective oscillation control for shock-capturing schemes. The work bridges the gap between existing linear or semi-discrete theories and practical fully discrete schemes with oscillation suppression.