偏微分方程数值方法中的有限元方法以及在特征值问题、弹性力学、电磁场问题、拓扑优化和反问题中的应用。
发表论文
27. Convergence analysis of an adaptive nonconforming FEM for phase-field dependent topology optimization in Stokes flow, with Bangti Jin, Jing Li and Shengfeng Zhu, accepted for publication in Mathematics of Computation, 2025. (preprint available at arXiv:2505.13776)
26. On the Crouzeix-Raviart finite element approximation of phase-field dependent topology optimization in Stokes flow, with Bangti Jin, Jing Li and Shengfeng Zhu, International Journal for Numerical Methods in Engineering, 126 (23), Article e70197 (25pp), 2025. (DOI: 10.1002/nme.70197, preprint available at arXiv:2505.04120)
25. Adaptive approximations of inclusions in a semilinear elliptic problem related to cardiac electrophysiology, with Bangti Jin and Fengru Wang, IMA Journal of Numerical Analysis, 2025. (early access with DOI: 10.1093/imanum/draf041)
24. Adaptive computation of elliptic eigenvalue topology optimization with a phase-field approach, with Jing Li and Shengfeng Zhu, Journal of Numerical Mathematics, 33 (4), 337-373, 2025. (DOI: 10.1515/jnma-2024-0060, preprint available at arXiv:2310.03970)
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 (13pp), 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 (27pp), 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, Article 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 Mathematics, 32 (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.