Yukun Li

Assistant Professor, University of Central Florida

Educations and Employments

• 2019-now, Assistant Professor in Mathematics

University of Central Florida, Orlando

• 2016-2019, Visiting Assistant Professor in Mathematics

The Ohio State University, Columbus

• 2015-2016, Postdoctoral Scholar in Mathematics

Pennsylvania State University, State College

• 2010-2015, Ph.D. in Mathematics

The University of Tennessee, Knoxville

Awards and Honors

Achievement Award Apr. 2015. Department of Mathematics, The University of Tennessee, Knoxville.

External and Internal Grants

External:

National Science Foundation REU (Senior Personnel) May 2023-May 2026. Award number: 2243772. 

Title: Research Experience for Undergraduates in Applied and Computational Mathematics.

National Science Foundation (Sole PI)  Jul. 2021-Jul. 2024. Award number: 2110728. 

Title: Numerical Methods for Deterministic and Stochastic Phase Field Models.

Internal:

Start-up Award Aug. 2019-Aug. 2021. Department of Mathematics, University of Central Florida, Orlando.

Research Interests

Continuous and Discontinuous Finite Element Methods

Numerical Solutions of Stochastic Ordinary and Partial Differential Equations

Adaptive Methods and Fast Solvers

Publications

1. Y. Li, C. Prachniak, and Y. Zhang, Analysis of a mixed finite element method for stochastic Cahn-Hilliard equation with multiplicative noise, accepted, Communications in Computational Physics, 2024.

2. Y. Li, L. Vo, and G. Wang, Higher order time discretization method for a class of semilinear stochastic partial differential equations with multiplicative noise, Journal of Computational and Applied Mathematics, 437:115442, 2024.

3. X. Feng, Y. Li, and Y. Lin, Fully discrete finite element methods for nonlinear stochastic elastic wave equations with multiplicative noise, Communications in Optimization Theory, 29: 1-38, 2022.

4. Y. Li, S. Wu, and Y. Xing, Finite element approximations of a class of nonlinear stochastic wave equation with multiplicative noise, Journal of Scientific Computing, 91(53), 2022.

5. A. Bousquet, Y. Li, and G. Wang, Some algorithms for the mean curvature flow under topological changes, Computational and Applied Mathematics, 40(104), 2021.

6. Y. Li and Y. Zhang, Analysis of adaptive two-grid finite element algorithms for linear and nonlinear problems, SIAM Journal on Scientific Computing, 43(2): 908-928, 2021. 

7. X. Feng, Y. Li, and Y. Zhang, Strong convergence of a fully discrete finite element method for a class of semilinear stochastic partial differential equations with multiplicative noise, Journal of Computational Mathematics, 39: 574-598, 2021.

8. X. Feng, Y. Li, and Y. Zhang, Fully discrete mixed finite element methods for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise, Journal of Scientific Computing, 83, 2020.

9. S. Wu and Y. Li, Analysis of the Morley element for the Cahn-Hilliard equation and the Hele-Shaw flow, ESAIM: Mathematical Modelling and Numerical Analysis, 54(3): 1025-1052, 2020.

10. Y. Li, Error analysis of a fully discrete Morley finite element approximation for the Cahn-Hilliard equation, Journal of Scientific Computing, 78(3): 1862-1892, 2019. 

11. C.-S. Chou, Y. Li, and D. Xiu, Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients, Journal of Computational Physics, 381: 52-66, 2019.

12. J. Xu, Y. Li, S. Wu, and A. Bousquet, On the stability and accuracy of partially and fully implicit schemes for phase field modeling, Computer Methods in Applied Mechanics and Engineering, 345: 826-853, 2019. 

13. M. Ozturk, M. Renardy, Y. Li, G. Agrawal and C.-S. Chou, A novel approach for handling soft error in conjugate gradients, 25th IEEE International Conference on High Performance Computing, Data, and Analytics, accepted (about 20% acceptance rate), 2018.

14. X. Feng, Z. Ge, and Y. Li, Analysis of a multiphysics finite element method for a poroelasticity model, IMA Journal of Numerical Analysis, 38(1): 330-359, 2018.

15. X. Feng, Y. Li, and Y. Zhang, Finite element methods for the stochastic Allen-Cahn equation with gradient-type multiplicative noises, SIAM Journal on Numerical Analysis, 55(1): 194-216, 2017. 

16. X. Feng, Y. Li, and Y. Xing, Analysis of mixed interior penalty discontinuous Galerkin methods for the Cahn-Hilliard equation and the Hele-Shaw flow, SIAM Journal on Numerical Analysis, 54(2): 825-847, 2016.

17. X. Feng and Y. Li, Analysis of interior penalty discontinuous Galerkin methods for the Allen-Cahn equation and the mean curvature flow, IMA Journal of Numerical Analysis, 35(4): 1622-1651, 2015.

18. X. Feng, Y. Li, and A. Prohl, Finite element approximations of the stochastic mean curvature flow of planar curves of graphs, Stochastic Partial Differential Equations: Analysis and Computations, 2(1): 54-83, 2014. 

19. H. Li and Y. Li, A discontinuous Galerkin finite element method for swelling model of polymer gels, Journal of Mathematical Analysis and Applications, 398(1): 11-25, 2013. 

20. H. Li and Y. Li, Optimal approximation to a class of nonlinear evolution equations, Applied Mathematics and Computation, 218(17): 8842-8852, 2012.

21. Y. Li, Numerical methods for deterministic and stochastic phase field models of phase transition and related geometric flows, Ph.D. Dissertation, 2015.

22. Y. Li, Learning rates of least-square regularized regression with polynomial kernel on the n-dimensional simplex, Master Thesis, 2010.

Skills

• Programming: Matlab, Comsol with Matlab, C++, C, Fortran, Python, MPI

• Software: Comsol, FEniCS, Freefem++, deal.II, MPICH2