Research Areas

1. Numerical analysis;

2. Uncertainty quantification;

3. Deep learning.

Publications

1. Superconvergent derivative recovery for Lagrange triangular elements of degree p on unstructured grids, R. E. Bank, J. Xu, and B. Zheng, SIAM Journal on Numerical Analysis, 45: 2032-2046, 2007.

2. A nonconforming finite element method for fourth order curl equations in R3, B. Zheng , Q. Hu, and J. Xu, Mathematics of Computation, 80: 1871-1886, 2011.

3. Adaptive mesh refinement and superconvergence for two dimensional interface problems, H. Wei, L. Chen, Y. Huang, and B. Zheng, SIAM Journal on Scientific Computing, 36: A1478-A1499, 2014.

4. Numerical solution of 3D Poisson-Nernst-Planck equations coupled with classical density functional theory for modeling ion and electron transport in a confined environment , D. Meng, B. Zheng, G. Lin, and M. L. Sushko, Communications in Computational Physics, 16: 1298-1322, 2014.

5. Quantifying the influence of conformational uncertainty in biomolecular solvation, H. Lei, X. Yang, B. Zheng, G. Lin, N. A. Baker, 2014, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 13:1327–1353, 2015.

6. Fast multilevel solvers for a class of discrete fourth order parabolic problems, B. Zheng, L.-P. Chen, X. Hu, L. Chen, R. H. Nochetto, and J. Xu, Journal of Scientific Computing, 69: 201–226, 2016.

7. Error analysis of finite element method for Poisson-Nernst-Planck equations, Y. Sun, P. Sun, B. Zheng, and G. Lin, Journal of Computational and Applied Mathematics, 301: 28–43, 2016.

8. A two-level stochastic collocation method for semilinear elliptic equations with random coefficients, L.-P. Chen, B. Zheng, G. Lin, and N. Voulgarakis, Journal of Computational and Applied Mathematics, 315: 195–207, 2017.

9. The THex algorithm and a simple Darcy solver on hexahedral meshes, G. Harper, J. Liu, and B. Zheng, Procedia Computer Science, 108C: 1903–1912, 2017.

10. An hp-adaptive minimum action method based on a posteriori error estimate, X. Wan, B. Zheng, and G. Lin, Communications in Computational Physics, 23: 408-439, 2018.

11. Field-warmed soil carbon changes imply high 21st-century modeling uncertainty, K. Todd-Brown，B. Zheng, T. W. Crowther, Biogeosciences, 15(12): 3659-3671, 2018.

12. Lowest-Order Weak Galerkin Finite Element Methods for Linear Elasticity on Rectangular and Brick Meshes, G. Harper, J. Liu, S. Tavener, and B. Zheng, Journal of Scientific Computing, 78(3): 1917–1941, 2019.

13. A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations. W. Hao, J. Hesthaven, G. Lin, B. Zheng. Journal of Scientific Computing, 82: 19, 2020.

14. 基于深度学习的ECG/PPG血压测量方法. 胡军锋, 郑彬. 生物医学工程研究, 41(1): 46-54, 2022.

15. Block triangular preconditioning for stochastic Galerkin method. D. Wang, B. Zheng, L. Chen, G. Lin, J. Xu, Journal of Computational and Applied Mathematics, 412: 114298, 2022.