Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium Session 185

Title: Discrete Hypocoercivity Estimates of Discontinuous Galerkin Methods for Vlasov-Poisson-Fokker-Planck equations

Speaker: Professor Xiong Tao (University of Science and Technology of China)

Time: 16:30–17:30, October 23, 2026

Location: Room 601, Huiyan Building, Yuehai Campus, Shenzhen University

Abstract:In this work, we develop and analyze a class of structure-preserving discontinuous Galerkin schemes for the nonlinear Vlasov-Poisson-Fokker-Planck model, reformulated as a hyperbolic system through a Hermite expansion in the velocity variable. We discretize the Vlasov-Fokker-Planck equation with the discontinuous Galerkin method, while the Poisson equation is approximated with either a discontinuous Galerkin method or a Raviart-Thomas mixed finite element method. We prove the exponential relaxation to equilibrium for suitable initial data, uniformly with respect to the discretization parameters thanks to discrete hypocoercivity arguments. Moreover, we check that the resulting semi-discrete schemes preserve the physical invariants along with the L2 variational structure of the linearized model. Numerical simulations verify the accuracy and the long-time behavior of the scheme.

Speaker Profile: Xiong Tao is a professor at the School of Mathematical Sciences, University of Science and Technology of China, and a recipient of the National High-Level Talent Award. His research focuses primarily on efficient and high-precision numerical methods for computational fluid dynamics and the equations of motion. In recent years, his research has centered on efficient, asymptotically well-preserved, low-rank algorithms for multiscale equations of motion. He has served as principal investigator on a General Program grant from the National Natural Science Foundation of China and has participated in key special projects funded by the Ministry of Science and Technology, among others.

All faculty and students are welcome!  

School of Mathematical Sciences  

October 19, 2026