High-Order and Adaptive Schemes for Nonlinear Hyperbolic PDEs

Workshop Title: High-Order and Adaptive Schemes for Nonlinear Hyperbolic PDEs

Dates: October 17-19, 2026

Description:

This workshop will bring together researchers working on the development, analysis, and application of modern high-order and adaptive numerical methods for nonlinear hyperbolic systems of PDEs. Such systems arise in a broad range of scientific and engineering applications, including fluid dynamics, plasma physics, geophysical flows, astrophysics, electromagnetism, traffic flow, multiphysics systems, and many others. Their accurate and efficient numerical approximation remains a major challenge due to the presence of shocks, discontinuities, multiscale structures, stiff regimes, and complex wave interactions.

The workshop aims to provide a forum for discussing recent advances in the design of robust, high-resolution numerical methods that combine accuracy, stability, adaptivity, and computational efficiency. Particular emphasis will be placed on modern reconstruction techniques, adaptive algorithms, structure-preserving methods, and schemes capable of handling challenging asymptotic and multiscale regimes.

The goals of the workshop are:

• To survey recent developments in high-order numerical methods for nonlinear hyperbolic PDEs
• To discuss adaptive strategies such as local polynomial adaptivity, smoothness indicators, mesh refinement, and moving-mesh techniques
• To explore structure-preserving formulations, including well-balanced, asymptotic-preserving, positivity-preserving, and entropy-stable schemes
• To foster interactions between numerical analysts, computational scientists, and application-driven researchers working on complex physical systems governed by hyperbolic PDEs
• To identify emerging challenges and future research directions in high-order and adaptive computational methods

• High-order methods for nonlinear hyperbolic systems of PDEs
• Smoothness indicators and local adaptivity techniques
• WENO, discontinuous Galerkin, central-upwind, active flux, and residual distribution methods
• Structure-preserving and asymptotic-preserving schemes
• Numerical methods for stiff and multiscale problems
• Nonconservative and multiphysics systems
• Well-balanced and positivity-preserving methods
• High-order methods on complex geometries and unstructured meshes
• Applications to compressible flows, shallow water models, magnetohydrodynamics, atmospheric science modeling, and related areas

The workshop will include invited lectures, contributed presentations, and discussions designed to encourage collaboration, exchange of ideas, and the development of new directions in the area of high-order and adaptive numerical methods for hyperbolic PDEs.

The list of Invited Speakers:

Remi Abgrall, University of Zurich, Switzerland and SUSTech, China

Remi Abgrall, University of Zurich, Switzerland and SUSTech, China

Alina Chertock, North Carolina State University, USA

Yibing Chen, Institute of Applied Physics and Computational Mathematics, China

Shaoshuai Chu, RWTH Aachen University, Germany

Wai Sun Don, Hong Kong Bartist University, Hong Kong

Michael Dumbser, University of Trento, Italy and SUSTech, China

Elena Gaburro, University of Verona, Italy

Yaguang Gu, South China University of Technology

Song Jiang, National Natural Science Foundation of China

Tatiana Kozubskaya, Keldysh Institute of Applied Mathematics, RAS, Russia

Tiegang Liu, Beihang University, China

Maria Lukacova, University of Mainz, Germany

Jianxian Qiu, Xiamen University, China

Huazhong Tang, Peking University, China

Davide Torlo, La Sapienza Università di Roma, Italy,

Bao-Shan Wang, Ocean University of China

Tao Xiong, University of Science and Technology of China