Dr. Jiashun Hu, The Hong Kong Polytechnic University

Weiying Zheng, Professor

Arbitrary Lagrangian–Eulerian Method for PDEs on Moving Domains

9:30-10:30 July 11(Friday), N202

Partial differential equations (PDEs) on moving domains arise in many applications, including geometric evolution, fluid–structure interaction, and interfacial fluid dynamics. A widely used computational framework for such problems is the arbitrary Lagrangian–Eulerian finite element method (ALE-FEM), developed since the 1980s. While ALE-FEM offers flexibility in handling mesh motion, it often suffers from mesh distortion over time, which can lead to numerical instability, even code breakdown, and poses challenges for the design of structure-preserving methods.

In this talk, I will discuss recent developments in ALE-FEM with a focus on mesh quality and strategies to address its deterioration. One strategy involves the use of tangential velocities governed by auxiliary PDEs to redistribute mesh points dynamically. Another incorporates sliding interface techniques into the ALE framework to better accommodate rotating boundaries. Both approaches are stable and enable rigorous error analysis. I will also discuss structure-preserving schemes, with applications to fluid–structure interaction and free-boundary problems involving interfacial forces.

Bio: Jiashun Hu is a Research Assistant Professor at the Hong Kong Polytechnic University since January 2025. He was a Postdoctoral Fellow at PolyU from 2021 to 2024. He received his Ph.D. in Mathematics from Tsinghua University in 2021, and his B.S. degree in Mathematics and Applied Mathematics from Tsinghua University in 2016. His research interests lie in the numerical analysis of partial differential equations, with a focus on surface evolution governed by geometric flows, fluid–structure interaction, and moving interface problems.