About me
Research Interests
● Approximation theory, Computational geometric flows, Numerical methods for PDEs including fractional PDEs.
Educational Background
● 2009. 9 - 2013. 7: M. Sci. in Applied Mathematics, School of Mathematics and Statistics, Central South University, Changsha, P.R. China;
● 2013. 9 - 2019. 7: Ph. D in Computational Mathematics, successive master-doctor program, School of Mathematics and Statistics, Central South University, Changsha, P.R. China;
● 2016. 9 - 2018. 7: Visiting student, Department of Mathematics, Texas A & M University, Texas, USA.
Working Experience
● 2019. 9 - 2021.8: Postdoc in Beijing Computational Science Research Center, Beijing & Shenzhen JL Computational Science and Applied Research Institute, Shenzhen. Supervisor: Prof. ZHANG Zhimin;
● 2021. 9 - now: MSU-BIT-SMBU Joint Research Center of Computational Mathematics, Shenzhen MSU-BIT University.
Selected Publications
[1] Duan Beiping, Zheng Zhoushun*, Cao Wen. Spectral approximation methods and error estimates for Caputo fractional derivative with applications to initial-value problems. Journal of Computational Physics, 319, 108-128(2016).
[2] Duan Beiping, Jin Bangti, Lazarov Raytcho*, Pasciak Joseph and Zhou Zhi. Space-time Petrov–Galerkin FEM for fractional diffusion problems. Computational Methods in Applied Mathematics, 18(1), 1-20(2018).
[3] Duan Beiping, Zheng Zhoushun*. An exponentially convergent scheme in time for time fractional diffusion equations with non-smooth initial data. Journal of Scientific Computing, 80, 717–742(2019).
[4] Duan Beiping, Lazarov Raytcho*, Pasciak Joseph. Numerical Approximation of Fractional Powers of Elliptic Operators. IMA Journal of Numerical Analysis, 40(3), 1746–1771(2020).
[5] Duan Beiping*, Zhang Zhimin. A rational approximation scheme for computing Mittag-Leffler function with discrete elliptic operator as input. Journal of Scientific Computing, 87 (2021)
[6] Duan Beiping, Li Buyang*, Zhang Zhimin. High-order fully discrete energy diminishing evolving surface finite element methods for a class of geometric curvature flows. Annals of Applied Mathematics, 37(4): 405-436(2021).
[7] Duan Beiping, Li Buyang, Yang Zongze*. An energy diminishing arbitrary Lagrangian-Eulerian finite element method for two-phase Navier-Stokes flow. Journal of Computational Physics, 2022.
[8] Duan Beiping*. Padé-parametric FEM approximation for fractional powers of elliptic operators on manifolds. IMA Journal of Numerical Analysis, 43(5): 2633-2664(2023).
[9] Duan Beiping, Yang Zongze*. A quadrature scheme for steady-state diffusion equations involving fractional power of regularly accretive operator. SIAM Journal on Scientific Computing, 45(5): A2226-A2249(2023).
[10] Duan Beiping, Li Buyang*. New artificial tangential motions for parametric finite element approximation of surface evolution. SIAM Journal on Scientific Computing, 46(1): A587-A608(2024).
[11] Liu Guidong, Liu Wenjie, Duan Beiping*. Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus. Advances in Computational Mathematics, 50, 68 (2024).
[12] Duan Beiping. Energy-stable and mesh-preserving parametric FEM for mean curvature flow of surfaces. SIAM Journal on Scientific Computing, 46(6): A3873-A3896.
[13] Duan Beiping. Mesh-preserving and energy-stable parametric FEM for geometric flows of surfaces. SIAM Journal on Numerical Analysis, 2025, 63(2): 619-640..
Foundings
High-order time parametric finite element methods for a class of curvature flows. NSFC, 300,000 RMB.