PI    NSFC Program, “Low-degree optimal finite element methods of non-Ciarlet type on unstructured grids”, (NSFC 12271512, 2023-2026),(independent score).

PI    NSFC Program, “Asymptotically structure-preserving order-reduced computational methods for fourth-order elliptic partial differential equations and related problems”, (NSFC 11871465, 2019-2022),(independent score).

PI    NSFC Program, “Finite element methods for elastic strain gradient problems”, (NSFC 11471026, 2015-2018).

PI    NSFC Program, “Optimal solvers for finite element system of fourth order problems”, (NSFC 11101415, 2012-2014).

PI    Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry Program, “Effective fast finite element methods for fourth order partial differential equation”, (Grant NO. Y390041G23),(independent score).

Ptcp(key member)    Major Research plan of the National Natural Science Foundation of China, “New framework for partial differential equations”, (NSFC92370205, 2024-2027).

Ptcp(key member)    Strategic Priority Research Program of Chinese Academy of Sciences, “Computing kernel for CAX integration in industral software”, (XDB 0640000, 2023-2027).

Ptcp(key member)    Strategic Priority Research Program of Chinese Academy of Sciences, “Formation, Evolution and Habitability of Terrestrial Planets”, (XDB 41020204, 2020-2024).

Dec 16-20, 2024    New Framework for Solving Partial Differential Equations and Mechine Learning, a Special Session in the The 14th AIMS Conference, Abu Dhabi, UAE, co-organizer.

Aug 22-25, 2024    Progress in Finite Element and Galerkin-type Methods, MS in the Jing-Jin-Ji plus Conference on Computational Mathematics, Huhhot, China, co-organizer.

Aug 28-29, 2023    Progress in Finite Element and Galerkin-type Methods, MS in the Jing-Jin-Ji plus Conference on Computational Mathematics, Taiyuan, China, co-organizer.

July 16-18, 2023    Eigenvalue problems: numerical methods and pplications, MS in the Annual Conference on Computational Mathematics 2023, Nanjing, China, co-organizer.

Oct 8-11, 2021        Eigenvalue problems in photonic and phononic, an 8-participant mini-symposium in the CSIAM Conference, Hefei, China, co-organizer.

Aug 16-19, 2021     Eigenvalue problems: numerical methods and pplications, an 8-participant mini-symposium in the Annual Conference on Computational Mathematics 2021, Nanjing, China, co-organizer(Delayed).

Sep 24-26, 2021      Finite Element, Discontinuous Galerkin and galerkin-type Methods, a mini-symposium in the Fifth Jing-Jin-Ji Conference on Conputational Mathematics, Zhangjiakou, China, co-organizer.

Aug 24-27, 2019     Finite Element, Discontinuous Galerkin and Galerkin-type Methods, an 11-participant mini-symposium in the FOurth Jing-Jin-Ji Conference on Computational Mathematics, Tianjin, China, co-organizer.

Aug 11-16, 2019     Multigrid methods for multiscale problems, a 2-session mini-symposium in International Multigrid Conference (IMG2019), Kunming, China, co-organizer.

July 15-19, 2019     Finite element exterior calculus and applications, a 4-session mini-symposium in 9th ICIAM, Valencia, Spain, co-organizer.

Oct 30-31, 2018      4th PKU Workshop on Numerical Methods for PDEs, Peking University, Beijing, co-organizer.

June 14-17, 2016    Efficient computing with finite element methods, a 4-session mini-symposium in MAFELAP, London, UK, co-organizer.

Aug 10-14, 2015      Numerical Methods for Multi-physics Problems, a 4-session mini-symposium in ICIAM 2015, Beijing, China, co-organizer.

July 6-10, 2015         Development on Non-Self-Similar Domain Decomposition and Multilevel Methods, a 3-session mini-symposium in DD23, Jeju, Korea, co-organizer. (Cancelled due to MERS)

(ORCID ID: 0000-0001-5490-5401) (*:corresponding author)(Google Scholar: https://scholar.google.com/citations?hl=zh-CN&user=RHYzbt4AAAAJ)

[Representative works]

1. Z., An optimal piecewise cubic nonconforming finite element scheme for the planar binarmonic equation on general triangulation, Science China Mathematics, 64(2021) 2579-2602.

2. Z., Minimal consistent finite element space for the biharmonic equation on quadrilateral grids, IMA Journal of Numerical Analysis, 40(2020), no. 2, 1390-1406.

3. Z., Regular decomposition and a framework of order reduced methods for fourth-order problems, Numerische Mathematik, 138(2018), 241-271.

4. Z., Mixed schemes for quad-curl equations, ESAIM: Mathematical Modelling and Numerical Analysis, 52(2018) 147-161.

5. Z., Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids, Numerische Mathematik 133(2016), 371-408.

6. Z. & Jinchao Xu: Optimal solvers for fourth-order PDEs discretized on unstructured grids, SIAM Journal on Numerical Analysis, 52(2014), 282-307.

7. Z. & Ming Wang: A nonconforming finite element method for the Cahn-Hilliard equation, Journal of Computational Physics 229(2010), 7361-7372.

[highlight papers]

8. Yingxia Xi, Xia Ji, Z.*: A multi-level mixed element scheme of the two dimensional Helmholtz transmission eigenvalue problem, IMA Journal of Numerical Analysis 40(2020), 686-707.

• Winner of the First-Class Award of Excellent Youth Paper of Chinese Computational Mathematical Society. August, 2019. (by Y. Xi)

9. Z., Ming Wang: A posterior estimator of nonconforming finite element method for fourth-order elliptic perturbation problems, Jurnal of Computational Mathematics 26(2008), 554-577.

• Winner of the Second-Class Award of Excellent Youth Paper of Chinese Computational Mathematical Society. November, 2007.

10. Huilan Zeng, Chensong Zhang, Z.*: Optimal quadratic element on rectangular grids for $H^1$ problems, BIT Numerical Mathematics, 61(2021) 665-689.

• Winner of the Second-Class Award of Excellent Youth Paper of Beijing Computational Mathematical Society. August, 2020. (by H. Zeng)

[Original peer-review papers]

11. Yifan Yue, Hongtao Chen, Z.: Lower and upper bounds for Stokes eigenvalues, Calcolo, 61:48(2024)

12. Bin Dai, Huilan Zeng, Chen-Song Zhang, Z.*: Lowest-degree robust finite element schemes for inhomogeneous bi-Laplace problems, Applied Numerical Mathematics, 203(2024)235-254

13. Huilan Zeng, Chen-Song Zhang, Z.*: On the existence of locally-defined projective interpolations, Applied Mathematics Letters, 146(2023), 108789

14. Qing Liu, Tiexiang Li, Z.: A mixed element scheme of Helmholtz transmission eigenvalue problem for anisotropic media, Inverse Problem 39(2023), Paper No. 055005, 17 pp..

15. Wenjia Liu, Z.*: A lowest-degree strictly conservative finite element scheme for incompressible Stokes problem on general triangulations, Journal of Scientific Computing, 93(2022):28.

16. Huilan Zeng, Chen-Song Zhang, Z.: A low-degree strictly conservative finite element method for incompressible flows on general triangulations, SMAI Journal of Computational Mathematics, 8(2022), 225-248.

17. Qi Jiang, Z., Lin Wan: Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data, PLOS Computational Biolugy, 18.1(2022): e1009821.

18. Qimeng Quan, Xia Ji, Z.*: A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials, Calcolo, 59(2022):5.

19. Yingxia Xi, Xia Ji, Z.: Order reduced schemes for fourth order eigenvalue problems on multiply-connected polygonal domains, Numerical Mathematics: Theory, Methods and Applications, 14(2021), No. 4, pp. 920-944.

20. Yingxia Xi, Xia Ji, Z.: A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem. Communications in Computational Physics, 30(2021), pp. 1061-1082.

21. Z., *Stable mixed element schemes for plate models on multiply-connected domains, Advances in Applied Mathematics and Mechanics, 12(2020), No. 4, pp. 1008-1034.

22. Yingxia Xi, Xia Ji, Z.: A high accuracy nonconforming finite element scheme for Helmholtz transmission eigenvalue problem, Journal of Scientific Computing (2020) 83:67.

23. Andrew Gilette, Kaibo Hu, Z.: Nonstandard finite element de Rham complexes on cubical meshes, BIT Numerical Mathematics 60(2020) 373-409.

24. Weifeng Zhang, Z.*: Order Reduced Method for Quad-curl Equation with Navier Type Boundary Condition, Journal of COmputational Mathematics, 38(2020) No.4, 565-579.

25. Ronghong Fan, Yanru Liu, Z.*: Mixed element methods for quad div equations, Computational Methods in Applied Mathematics, 19(2019), N0. 2, 341-357.

26. Wei Gong, Zhiyu Tan, Z.*: A robust block diagonal preconditioner for elliptic optimal control problems with mixed finite element method, Numerical Linear Algebra and Application, 25(2018), e2129.

27. Fei Wang, Z.*: Optimal Quadratic Nitsche Extend Finite Element Method for Interface Problem of DIffusion Equation, Journal of Computational Mathematics, Vol. 36(2018), 693-717.

28. Z., Yingxia Xi, Xia Ji: *A multi-level mixed element method for the eigenvalue problem of biharmonic equation, Journal of Scientific Computing, 75(2018), 1415-1444.

29. Yuyan Chen, Z.*: A conservative stable finite element method for Stokes flow and nearly incompressible linear elasticity on rectangular grid, Journal of Computational and Applied Mathematics, 323(2017), 53-70.

30. Zheng Li, Z.*: A stable mixed element method for biharmonic equation with first-order function spaces, Computational Methods in Applied Mathematics, 17(2017), no. 4, 601-616.

31. Shangyou Zhang, Z.*: $C_0P_2-P_0$ Stokes finite element pair on sub-hexhadron tetrahedral grids, Calcolo, 54(2017), no. 4, 1403-1417.

32. Jun Hu, Xueqin Yang, Z.*: Capacity of the Adini element for biharmonic equations, Journal of Scientific Computing, 69(2016), 1366-1383.

33. Chunsheng Feng, Z.*: Optimal solver for Morley element problem for biharmonic equation on shape-regular grids, Journal of Computational Mathematics 34(2016), 159-173.

34. Xiangyun Meng, Xueqin Yang, Z.*: *Convergence analysis of the rectangular Morely element scheme for second-order problem in arbitary dimensions, Science China Mathematics, 59(2016), 2245-2264.

35. Ruth Jinru Cheng, Xuehai Huang, Shi Shu, Jinchao Xu, Chensong Zhang, Z.*, Zhiyang Zhou: Application of an energy minimizing algebraic multigrid method for subsurface water simulation, Int. J. Numer. Anal. Model. 10(2013), 374-388.

36. Ming Wang, Penghe Zu, Z.*: High Accurancy Nonconforming FInite Element Methods for fourth-order Problems, Science China Mathematics 55(2012), 2183-2192.

37. Jinchao Xu, Z.: Norms of discrete trace functions of $H^1(\Omega)$ and $H^2(\Omega)$, COmputational Methods in Applied Mathematics 12(2012), 4, 500-512.

38. Boran Gao, Z., Ming Wang: A note on the nonconforming ffinite elements for elliptic problems, Journal of Computational Mathematics 29(2011), 215-226.

[Original peer-review book chapters]

39. Huiwen Wu, Z.*: A Variational Approach to Personalized Federated Learning and Its Improvement, in Knowledge Management and Acqusition for Intelligent Systems, PKAW 2024, LNAI 15372, 2024.
40. Jinchao Xu, Z.: Optimal finite element methods for interface problems, in Proceeding of the 22nd International Conference of Domain Deconposition, 77-91, Springer International Publishing, 2016.