Finite element analysis, adaptive finite element methods including mixed, discontinuous Galerkin and nonconforming methods, and applications in eigenvalue problems, elasticity, electromagnetism, topology optimization and inverse problems.

Publications

24. Adaptive computation of elliptic eigenvalue topology optimization with a phase-field approach, with Jing Li and Shengfeng Zhu, Journal of Numerical Mathematics, 2025. (early access with DOI: 10.1515/jnma-2024-0060)   

23. Adaptive finite element approximations of the first eigenpair associated with p-Laplacian, with Guanglian Li, Jing Li, Julie Merten and Shengfeng Zhu, SIAM Journal on Scientific Computing, 47 (1), A374-A402, 2025. (DOI: 10.1137/24M1637052) 

22. Discontinuous polynomial approximation in electrical impedance tomography with total variational regularization, with Bangti Jin, Jingrong Yang and Kai Zhang, Communications in Nonlinear Science and Numerical Simulation, 157, Article 108166, 2024. (DOI: 10.1016/j.cnsns.2024.108166)   

21. An adaptive phase-field method for structural topology optimization, with Bangti Jin, Jing Li and Shengfeng Zhu,  Journal of Computational Physics, 506, Article 112932, 2024. (DOI: 10.1016/j.jcp.2024.112932)

20. An adaptive edge element approximation of a quasilinear H(curl)-elliptic problem, with Irwin Yousept and Jun Zou, Mathematical Models and Methods in Applied Sciences, 30 (14), 2799-2826, 2020. (DOI: 10.1142/S0218202520500554)

19. Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity, with Bangti Jin, Inverse Problems, 36, 014003 (28pp), 2020. (DOI: 10.1088/1361-6420/ab261e)

18. Quasi-optimality of an adaptive finite element method for cathodic protection, with Guanlian Li, ESAIM: Mathematical Modelling and Numerical Analysis, 53 (5), 1645-1665, 2019. (DOI: 10.1051/m2an/2019031)

17. The decoupling of elastic waves from a weak formulation perspective,with Junjiang Lai, Hongyu Liu and Jingni Xiao, East Asian Journal on Applied Mathematics 9 (2), 241-251, 2019. (DOI: 10.4208/eajam.080818.121018)

16. A convergent adaptive finite element method for electrical impedance tomography, with Bangti Jin and Jun Zou, IMA Journal of Numerical Analysis 37 (3), 1520-1550, 2017. (DOI: 10.1093/imanum/drw045)

15. A convergent adaptive edge element method for an optimal control problem in magnetostatics, with Jun Zou, ESAIM: Mathematical Modeling and Numerical Analysis 51 (2), 615-640, 2017. (DOI: 10.1051/m2an/2016030)

14. A convergent adaptive finite element method for cathodic protection, with Guanglian Li, Computational Methods in Applied Mathematics 17 (1), 105-120, 2017. (DOI: 10.1515/cmam-2016-0032)

13. Convergence of an adaptive finite element method for distributed flux reconstruction, with Jun Zou, Mathematics of Computation 84 (296), 2645–2663, 2015. (DOI: 10.1090/mcom/2961)

12. Analysis of an adaptive finite element method for recovering the Robin coefficient,with Jun Zou, SIAM Journal on Control and Optimization 53 (2), 622-644, 2015.

11. A posteriori error estimates for local C⁰ discontinuous Galerkinmethods for Kirchhoff plate bending problems, with Jianguo Huang and Xuehai Huang, Journal of Computational Mathematics32 (6), 665-686, 2014.

10. An adaptive edge element method and its convergence for a saddle-point problem from magnetostatics, with Junqing Chen and Jun Zou, Numerical Methods for Partial Differential Equations 28 (5), 1643-1666, 2012.

9. A class of high order adaptive mixed element methods for Kirchhoff plate bending problems, with Jianguo Huang, Science China Mathematics (Chinese version) 42 (5), 473-489, 2012. (in Chinese)

8. Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation, with Jianguo Huang, Science China Mathematics 55 (5), 1083-1098, 2012. 

7. A posteriori error estimates for local discontinuous Galerkin methods of linear elasticity, with Yuncheng Chen and Jianguo Huang, Journal of Shanghai Jiao Tong University 45 (12), 1857-1862, 2011. (in Chinese)

6. Convergence of an adaptive mixed finite element method for Kirchhoff plate bending problems, with Jianguo Huang and Xuehai Huang, SIAM Journal on Numerical Analysis 49 (2), 574-607, 2011.

5. On the local discontinuous Galerkin method for linear elasticity, with Yuncheng Chen, Jianguo Huang, and Xuehai Huang, Mathematical Problems in Engineering 2010, Article ID 759547, DOI:10.1155/2010/759547, 2010.

4. An adaptive inverse iteration for Maxwell eigenvalue problem based on edge elements, with Junqing Chen and Jun Zou, Journal of Computational Physics 229 (7), 2649-2658, 2010.

3. Convergence analysis of an adaptive edge element method for Maxwell’s equations, with Junqing Chen and Jun Zou, Applied Numerical Mathematics 59 (12), 2950-2969, 2009.

2. Finite element analysis for general elastic multi-structures, with Jianguo Huang and Zhongci Shi, Science in China Series A, 49 (1), 109-129, 2006.

1. Some studies on mathematical models for general elastic multi-structures, with Jianguo Huang and Zhongci Shi, Science in China Series A, 48 (7), 986-1007, 2005.

Research Grants

1. Natural Science Foundation of Shanghai Grant, May 2017 - April 2020, PI.

2. National Natural Science Foundation of China Grant, Jan 2013 - Dec 2015, PI.

3. Ministry of Education ofthe People’s Republic of China Specialized Research Fund for the Doctoral Program of  Higher Education, Jan 2013 - Dec 2015, PI.

4. Innovation Program of Shanghai Municipal Education Commission, Jan 2013 - Dec 2015, PI.

5. Shanghai Normal University Research Program, Jan 2012 - Dec 2013, PI.