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High Order Entropy Stable Discontinuous Galerkin Discretizations

AMS Seminar Series

Speaker: Jesse Chan, Department of Computational Applied Mathematics and Operations Research, Rice University

Presentation

Seminar Slide Deck (PDF-48MB)

Abstract

High order discontinuous Galerkin (DG) methods combine high order accuracy and geometric flexibility with a computationally convenient structure. However, high order methods are known to be unstable when applied to nonlinear conservation laws whose solutions exhibit shocks and 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 the construction of robust entropy stable discontinuous Galerkin methods, as well as extensions of entropy stable formulations to positivity preserving schemes.

Biography

Photo of Jesse Chan
Jesse Chan is an associate professor in the Department of Computational Applied Mathematics and Operations Research at Rice University. He received his Ph.D. from the University of Texas at Austin in 2013, and was a postdoc at Rice University from 2013-2015 and Virginia Tech from 2015-2016. He returned to Rice as faculty in 2016 and was awarded an NSF CAREER Award in 2020. His research focuses on the construction of provably stable high order accurate numerical methods for the time-dependent partial differential equations in fluid dynamics.