Fengyan Li

Professor, Mathematical Sciences

Dr. Fengyan Li received her BS and MS degrees in Computational Mathematics from Peking University in 1997 and 2000, respectively, and her PhD degree in Applied Mathematics from Brown University in 2004. Before she joined RPI in 2006, she held a postdoc position at University of South Carolina.

Dr. Li's research interests and activities are mainly in Numerical Analysis and Scientific Computing. Her research focuses on the design and analysis of robust and highly accurate computational methods, especially discontinuous Galerkin finite element methods, with applications such as in wave propagation, fluid dynamics, optimal control, plasma physics, astrophysics, and nonlinear optics. Dr. Li received a Stella Dafermos Award at Brown University in 2004, and was a recipient of Alfred P. Sloan Research Fellowship in 2008. In 2009, she was granted an NSF-CAREER award for her research in high order methods and their applications. Dr. Li is currently serving on the editorial board of SIAM Journal of Numerical Computing and Applied Mathematics and Mechanics (English Edition)

Dr. Li has been actively involved in Association for Women in Mathematics (AWM) and Women in Numerical Analysis and Scientific Computing (WINASC) Research Network.  In 2015, she co-organized a mini-symposium and served as a career panelist at the 8th International Congress on Industrial and Applied Mathematics (ICIAM) in Beijing (China), she was also an invited speaker at the workshop “Women in Applied Maths & Soft Matter Physics" in Mainz (Germany);  She has been serving as a mentor through AWM Mentor Network since 2011, and as a faculty advisor of the AWM Student Chapter at RPI since 2016.  Dr. Li is currently a member of the Steering Commitee of WINASc. 

 

Education

Ph.D. in Applied Mathematics, Brown University, 2004

M.S. in Computational Mathematics, Peking University, 2000

B.S. in Computational Mathematics, Peking University, 1997

Research Focus
  • Discontinuous Galerkin methods; Finite element methods
  • High order methods for MHD, Hamilton-Jacobi, Maxwell's in linear and nonlinear media, Vlasov-Maxwell equations, multi-scale kinetic models, fluid models
  • High order structure-preserving methods
Select Works
  • V. A. Bokil, Y. Cheng, Y. Jiang, F. Li, Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media, Journal of Computational Physics, v350 (2017), pp.420-452
  • H. Yang and F. Li, Discontinuous Galerkin methods for relativistic Vlasov-Maxwell system, Journal of Scientific Computing,v73 (2017), pp.1216-1248
  • M. Li, P. Guyenne, F. Li and L. Xu, A positivity-preserving well-balanced central discontinuous Galerkin method for the nonlinear shallow water equations, Journal of Scientific Computing, v71 (2017), pp.994-1034
  • Y. Cheng, C.-S. Chou, F. Li, Y. Xing, L2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations, Mathematics of Computation, v86 (2017), pp.121-155
  • M. Li, F. Li, Z. Li, L. Xu, Maximum-principle-satisfying and positivity-preserving high order central DG methods for hyperbolic conservation laws, SIAM Journal on Scientific Computing, v38 (2016), pp.A3720-A3740
  • H. Yang and F. Li, Stability analysis and error estimates of an exactly divergence-free method for the magnetic induction equations, ESAIM: Mathematical Modelling and Numerical Analysis, v50 (2016), pp.965-993
  • T. Xiong, J. Jang, F. Li, J.-M. Qiu, High order asymptotic preserving nodal discontinuous Galerkin IMEX schemes for the BGK equation, Journal of Computational Physics, v284 (2015), pp.70-94
  • Y. Cheng, I. Gamba, F. Li, and P. Morrison, Discontinuous Galerkin methods for Vlasov-Maxwell equations, SIAM Journal on Numerical Analysis, v52-2 (2014), pp.1017-1049