Conference Summary
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:
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To survey recent developments in high-order numerical methods for nonlinear hyperbolic PDEs
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To discuss adaptive strategies such as local polynomial adaptivity, smoothness indicators, mesh refinement, and moving-mesh techniques
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To explore structure-preserving formulations, including well-balanced, asymptotic-preserving, positivity-preserving, and entropy-stable schemes
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To foster interactions between numerical analysts, computational scientists, and application-driven researchers working on complex physical systems governed by hyperbolic PDEs
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To identify emerging challenges and future research directions in high-order and adaptive computational methods
Topics may include (but are not limited to):
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High-order methods for nonlinear hyperbolic systems of PDEs
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Smoothness indicators and local adaptivity techniques
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WENO, discontinuous Galerkin, central-upwind, active flux, and residual distribution methods
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Structure-preserving and asymptotic-preserving schemes
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Numerical methods for stiff and multiscale problems
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Nonconservative and multiphysics systems
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Well-balanced and positivity-preserving methods
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High-order methods on complex geometries and unstructured meshes
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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
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
Lorenzo Micalizzi, North Carolina State University, USA
Gabriella Puppo, La Sapienza Università di Roma, Italy
Jianxian Qiu, Xiamen University, China
Huazhong Tang, Peking University, China
Bao-Shan Wang, Ocean University of China
Tao Xiong, University of Science and Technology of China
Yan Xu, University of Science and Technology of China