Finite element analysis, adaptive finite element methods including mixed, discontinuous Galerkin and nonconforming methods, and applications in elasticity, electromagnetism and inverse problems.
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Research Direction:
Finite element analysis, adaptive finite element methods including mixed, discontinuous Galerkin and nonconforming methods, and applications in elasticity, electromagnetism and inverse problems. Academic Achievement:
Publications 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. Teaching WORK:
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