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math.NA2026
Novel Adaptive Methods for Hyperbolic Conservation Laws Based on New Quasi-Linear Seventh- and Ninth-Order Schemes
Shaoshuai Chu, Pingyao Feng, Vadim A. Kolotilov +2
We develop new adaptive numerical schemes for one- and two-dimensional hyperbolic systems of conservation laws. The methodology relies on the use of a smoothness indicator to autom…
math.NA2026
Adaptive Artificial Anti-Diffusion Methods for Hyperbolic Systems of Conservation Laws
Shaoshuai Chu, Igor Kliakhandler, Alexander Kurganov
We introduce new adaptive artificial anti-diffusion (AAAD) methods for one- and two-dimensional hyperbolic systems of conservation laws. The key idea is to reduce the amount of num…