Upcoming Event: Babuška Forum

High order entropy stable discretizations of nonlinear conservation laws

Jesse Chan, Oden Institute

Abstract

High order numerical methods are well-suited to resolving time-dependent vorticular flows due to their low numerical dissipation and dispersion. However, high order methods are known to be unstable when applied to nonlinear conservation laws whose solutions exhibit shocks and other under-resolved solution features. Entropy stable schemes address this instability by ensuring that physically relevant solutions satisfy a semi-discrete entropy inequality independently of numerical resolution and additional stabilization while retaining formal high order accuracy. In this talk, we will review both traditional heuristic stabilization methods and some recent techniques for constructing robust entropy stable discontinuous Galerkin finite element methods and reduced order models.

Biography

Jesse Chan is an associate professor at the Oden Institute for Computational Engineering & Sciences and in the Department of Aerospace Engineering and Engineering Mechanics at UT Austin. He received his PhD in Computational Science, Engineering, and Mathematics from the University of Texas at Austin in 2013 working on high order adaptive finite element methods for steady compressible fluid flows. After postdoc positions at Rice University (2013-2015) and Virginia Tech (2015-2016), he rejoined Rice as a faculty member in the Department of Computational Applied Mathematics and Operations Research (previously Computational and Applied Mathematics) at Rice University in 2016. In 2025, he moved back to UT Austin. His research focuses on the accurate and efficient numerical solution of time-dependent hyperbolic partial differential equations, in particular the construction and analysis of provably stable high order methods for fluid dynamics.