4 papers · 1 filter
Fully Discrete Multi-Entropy Stability of High-Order Schemes for Compressible MHD: A Weak-to-Strong Framework
Huihui Cao, Kailiang Wu, Caiyou Yuan
We establish a fully discrete weak-to-strong (W2S) multi-entropy stability theory for arbitrarily high-order finite-volume and discontinuous Galerkin (DG) approximations of the ide…
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…
Compact Finite-Average-Moment Schemes with Single-Step Oscillation Elimination for Hyperbolic Conservation Laws
Chuan Fan, Kailiang Wu
High-order shock-capturing schemes often face severe computational bottlenecks due to wide stencils, stagewise nonlinear weights, and expensive local characteristic decompositions.…
Hidden Accuracy and Superconvergence Analysis of Central Discontinuous Galerkin Methods on Overlapping Meshes
Manting Peng, Kailiang Wu
This paper establishes the first rigorous superconvergence theory for semidiscrete and fully discrete central discontinuous Galerkin (CDG) methods for linear hyperbolic equations o…