计算流体力学和磁流体力学，智能化流体,  有限元方法及其应用，自适应算法, 流体优化控制，数据同化

2019-04--  中国科学院数学与系统科学研究院 研究员

2015-10-- 中国科学院大学 岗位教授

2014-02--2019-03 中国科学院数学与系统科学研究院 副研究员

2013-04--2014-02 中国科学院数学与系统科学研究院计算数学所 副研究员

2008-07--2013-04 中国科学院数学与系统科学研究院 助理研究员

2010-05--2012-05 瑞士ETH Zurich (苏黎世联邦理工学院)  高级研究助理

2008-10--2010-05 法国INRIA (信息与自动化国家研究院)  Postdoctoral  Fellow

2019-07--2019-09, Queensland University of Technology, invited Professor

2017-11--2017-12, The Hong Kong Polytechnic University, invited Professor

2018-09--2008-10  Université de Pau， France， invited Professor

2008-07--2008-08   Université de Valenciennes， France，invited  Professor

2007-05--2007-07   Université de Pau， France， invited Professor

   

   

[1] Hao, Tingting, Guan, Xiaofei, Mao, Shipeng, Chen, Shaochun. Computable Interpolation Error Constants for the Geometric Simplex Finite Elements. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2021, 87(1): https://www.webofscience.com/wos/woscc/full-record/WOS:000628456800001.
[2] M Riaz Khan, M. Li, Shipeng Mao, R.Ali, S. Khan. Comparative study on heat transfer and friction drag in the flow of various hybrid nanofluids effected by aligned magnetic field and nonlinear radiation. SCIENTIFIC REPORTS[J]. 2021, 11(1): [3] 毛士鹏. Error estimate of a fully discrete finite element method for incompressible vector potential magnetohydrodynamic system. Journal of Scientific Computing. 2021, [4] Yang, Jinjin, Mao, Shipeng. Second order fully decoupled and unconditionally energy-stable finite element algorithm for the incompressible MHD equations. APPLIED MATHEMATICS LETTERS[J]. 2021, 121: http://dx.doi.org/10.1016/j.aml.2021.107467.
[5] Ding, Qianqian, Mao, Shipeng. A Convergent Finite Element Method for the Compressible Magnetohydrodynamics System. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2020, 82(1): https://www.webofscience.com/wos/woscc/full-record/WOS:000514406700001.
[6] Ding, Qianqian, Long, Xiaonian, Mao, Shipeng. Convergence analysis of Crank-Nicolson extrapolated fully discrete scheme for thermally coupled incompressible magnetohydrodynamic system. APPLIED NUMERICAL MATHEMATICS[J]. 2020, 157: 522-543, http://dx.doi.org/10.1016/j.apnum.2020.06.018.
[7] Zhao, Jikun, Zhang, Bei, Mao, Shipeng, Chen, Shaochun. The nonconforming virtual element method for the Darcy-Stokes problem. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING[J]. 2020, 370: http://dx.doi.org/10.1016/j.cma.2020.113251.
[8] Yang, Jinjin, Mao, Shipeng, He, Xiaoming, Yang, Xiaofeng, He, Yinnian. A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING[J]. 2019, 356: 435-464, http://ir.amss.ac.cn/handle/2S8OKBNM/35617,.
[9] Zhao, Jikun, Zhang, Bei, Mao, Shipeng, Chen, Shaochun. THE DIVERGENCE-FREE NONCONFORMING VIRTUAL ELEMENT FOR THE STOKES PROBLEM. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2019, 57(6): 2730-2759, https://www.webofscience.com/wos/woscc/full-record/WOS:000546984300009.
[10] Su, Haiyan, Mao, Shipeng, Feng, Xinlong. Optimal Error Estimates of Penalty Based Iterative Methods for Steady Incompressible Magnetohydrodynamics Equations with Different Viscosities. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2019, 79(2): 1078-1110, [11] Zhao, Jikun, Zhang, Bei, Chen, Shaochun, Mao, Shipeng. The Morley-Type Virtual Element for Plate Bending Problems. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2018, 76(1): 610-629, https://www.webofscience.com/wos/woscc/full-record/WOS:000434711800023.
[12] Hiptmair, Ralf, Li, Lingxiao, Mao, Shipeng, Zheng, Weiying. A fully divergence-free finite element method for magnetohydrodynamic equations. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES[J]. 2018, 28(4): 659-695, https://www.webofscience.com/wos/woscc/full-record/WOS:000432721600002.
[13] Ren, Jincheng, Mao, Shipeng, Zhang, Jiwei. Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS[J]. 2018, 34(2): 705-730, https://www.webofscience.com/wos/woscc/full-record/WOS:000423435500014.
[14] Li, Xujing, Mao, Shipeng, Yang, Kangkang, Zheng, Weiying. On the Magneto-Heat Coupling Model for Large Power Transformers. COMMUNICATIONS IN COMPUTATIONAL PHYSICS[J]. 2017, 22(3): 683-711, https://www.webofscience.com/wos/woscc/full-record/WOS:000404993500004.
[15] Zhang, Bei, Chen, Shaochun, Zhao, Jikun, Mao, Shipeng. A posteriori error analysis of nonconforming finite element methods for convection-diffusion problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2017, 321: 416-426, http://dx.doi.org/10.1016/j.cam.2017.03.002.
[16] Ren, Jincheng, Long, Xiaonian, Mao, Shipeng, Zhang, Jiwei. Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2017, 72(3): 917-935, https://www.webofscience.com/wos/woscc/full-record/WOS:000408109600001.
[17] Zhao, Jikun, Mao, Shipeng, Zheng, Weiying. Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers. APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION[J]. 2016, 37(11): 1479-1500, http://lib.cqvip.com/Qikan/Article/Detail?id=670413849.
[18] Hiptmair, Ralf, JerezHanckes, Carlos, Mao, Shipeng. EXTENSION BY ZERO IN DISCRETE TRACE SPACES: INVERSE ESTIMATES. MATHEMATICS OF COMPUTATION[J]. 2015, 84(296): 2589-2615, https://www.webofscience.com/wos/woscc/full-record/WOS:000369811600002.
[19] Zhao, Jikun, Chen, Shaochun, Zhang, Bei, Mao, Shipeng. Robust a posteriori error estimates for conforming and nonconforming finite element methods for convection-diffusion problems. APPLIED MATHEMATICS AND COMPUTATION[J]. 2015, 264: 346-358, https://www.webofscience.com/wos/woscc/full-record/WOS:000355553000028.
[20] Zhao, Jikun, Chen, Shaochun, Zhang, Bei, Mao, Shipeng. Robust a Posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients on Anisotropic Meshes. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2015, 64(2): 368-400, https://www.webofscience.com/wos/woscc/full-record/WOS:000357343600004.
[21] Li, Mingxia, Mao, Shipeng, Zhang, Shangyou. New error estimates of nonconforming mixed finite element methods for the Stokes problem. MATHEMATICAL METHODS IN THE APPLIED SCIENCES[J]. 2014, 37(7): 937-951, https://www.webofscience.com/wos/woscc/full-record/WOS:000334157200001.
[22] Li, Mingxia, Guan, Xiaofei, Mao, Shipeng. New error estimates of the Morley element for the plate bending problems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2014, 263: 405-416, https://www.webofscience.com/wos/woscc/full-record/WOS:000332135300032.
[23] Li, Mingxia, Guan, Xiaofei, Mao, Shipeng. CONVERGENCE AND SUPERCONVERGENCE ANALYSIS OF LAGRANGE RECTANGULAR ELEMENTS WITH ANY ORDER ON ARBITRARY RECTANGULAR MESHES. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2014, 32(2): 169-182, http://ir.amss.ac.cn/handle/2S8OKBNM/47855, http://www.irgrid.ac.cn/handle/1471x/6871160, http://ir.amss.ac.cn/handle/2S8OKBNM/47856.
[24] Li, Mingxia, Li, Jingzhi, Mao, Shipeng. Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction. COMMUNICATIONS IN COMPUTATIONAL PHYSICS[J]. 2014, 15(4): 1068-1090, https://www.webofscience.com/wos/woscc/full-record/WOS:000340781300012.
[25] Li, Mingxia, Mao, Shipeng. Anisotropic interpolation error estimates via orthogonal expansions. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS[J]. 2013, 11(4): 621-629, https://www.webofscience.com/wos/woscc/full-record/WOS:000314181200004.
[26] Li, Mingxia, Li, Jingzhi, Mao, Shipeng. A PRIORI ERROR ESTIMATES OF A FINITE ELEMENT METHOD FOR DISTRIBUTED FLUX RECONSTRUCTION. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2013, 31(4): 382-397, http://ir.amss.ac.cn/handle/2S8OKBNM/37065, http://www.irgrid.ac.cn/handle/1471x/6870960, http://ir.amss.ac.cn/handle/2S8OKBNM/37066.
[27] Li JingZhi, Liu HongYu, Mao ShiPeng. Approximate acoustic cloaking in inhomogeneous isotropic space. SCIENCE CHINA-MATHEMATICS[J]. 2013, 56(12): 2631-2644, http://ir.amss.ac.cn/handle/2S8OKBNM/49744, http://www.irgrid.ac.cn/handle/1471x/6871187, http://ir.amss.ac.cn/handle/2S8OKBNM/49745.
[28] Li, Mingxia, Mao, Shipeng. A new a priori error analysis of nonconforming and mixed finite element methods (vol 26, pg 35, 2013). APPLIED MATHEMATICS LETTERSnull. 2013, 26(2): 313-313, https://www.webofscience.com/wos/woscc/full-record/WOS:000311243900024.
[29] Hiptmair, Ralf, Mao, Shipeng. Stable multilevel splittings of boundary edge element spaces. BIT NUMERICAL MATHEMATICS[J]. 2012, 52(3): 661-685, http://dx.doi.org/10.1007/s10543-012-0369-1.
[30] Chen Shaochun, Zheng Yanjun, Mao Shipeng. NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS. 数学物理学报：B辑英文版. 2011, 31(3): 815-825, http://lib.cqvip.com/Qikan/Article/Detail?id=37887457.
[31] Li, Mingxia, Chen, Hongtao, Mao, Shipeng. ACCURACY ENHANCEMENT FOR THE SIGNORINI PROBLEM WITH FINITE ELEMENT METHOD. ACTA MATHEMATICA SCIENTIA[J]. 2011, 31(3): 897-908, http://lib.cqvip.com/Qikan/Article/Detail?id=37887463.
[32] Becker Roland, Mao Shipeng. Quasi-optimality of an Adaptive Finite Element Method for an Optimal Control Problem. Computational Methods in Applied Mathematics[J]. 2011, [33] Becker, Roland, Mao, Shipeng. QUASI-OPTIMALITY OF ADAPTIVE NONCONFORMING FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2011, 49(3): 970-991, https://www.webofscience.com/wos/woscc/full-record/WOS:000292033100003.
[34] Li, Mingxia, Becker, Roland, Mao, Shipeng. A remark on supercloseness and extrapolation of the quadrilateral Han element for the Stokes equations. COMPTES RENDUS MATHEMATIQUE[J]. 2011, 349(17-18): 1017-1020, https://www.webofscience.com/wos/woscc/full-record/WOS:000297239800020.
[35] Chen Shaochun, Zheng Yanjun, Mao Shipeng. NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS. ACTA MATHEMATICA SCIENTIA[J]. 2011, 31(3): 815-825, http://lib.cqvip.com/Qikan/Article/Detail?id=37887457.
[36] Chen, Shaochun, Zheng, Yanjun, Mao, Shipeng. Anisotropic error bounds of Lagrange interpolation with any order in two and three dimensions. APPLIED MATHEMATICS AND COMPUTATION[J]. 2011, 217(22): 9313-9321, https://www.webofscience.com/wos/woscc/full-record/WOS:000290902600043.
[37] Mao ShiPeng, Shi ZhongCi. On the error bounds of nonconforming finite elements. SCIENCE CHINA-MATHEMATICS[J]. 2010, 53(11): 2917-2926, https://www.webofscience.com/wos/woscc/full-record/WOS:000284382200010.
[38] Mao, Shipeng, Nicaise, Serge, Shi, ZhongCi. ERROR ESTIMATES OF MORLEY TRIANGULAR ELEMENT SATISFYING THE MAXIMAL ANGLE CONDITION. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING[J]. 2010, 7(4): 639-655, https://www.webofscience.com/wos/woscc/full-record/WOS:000277127400003.
[39] 毛士鹏. Adaptive nonconforming finite elements for the Stokes equations. Bol. Soc. Esp. Mat. Apl. SeMA. 2010, [40] Mao, Shipeng, Zhao, Xuying, Shi, Zhongci. Convergence of a standard adaptive nonconforming finite element method with optimal complexity. APPLIED NUMERICAL MATHEMATICS[J]. 2010, 60(7): 673-688, https://www.webofscience.com/wos/woscc/full-record/WOS:000278860100002.
[41] Chen, Shaochun, Ren, Guobiao, Mao, Shipeng. Second-order locking-free nonconforming elements for planar linear elasticity. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2010, 233(10): 2534-2548, https://www.webofscience.com/wos/woscc/full-record/WOS:000274554900009.
[42] Becker, Roland, Mao, Shipeng, Shi, Zhongci. A CONVERGENT NONCONFORMING ADAPTIVE FINITE ELEMENT METHOD WITH QUASI-OPTIMAL COMPLEXITY. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2010, 47(6): 4639-4659, https://www.webofscience.com/wos/woscc/full-record/WOS:000277836100027.
[43] Xuying Zhao, Shipeng Mao, Zhong-Ci Shi. ADAPTIVE QUADRILATERAL AND HEXAHEDRAL FINITE ELEMENT METHODS WITH HANGING NODES AND CONVERGENCE ANALYSIS. 计算数学：英文版. 2010, 621-644, http://lib.cqvip.com/Qikan/Article/Detail?id=35211950.
[44] 毛士鹏. On the superconvergence of bilinear finite element for second order elliptic problems with general boundary conditions. Int. J. Inf. Syst. Sci.. 2010, [45] Zhao, Xuying, Mao, Shipeng, Shi, ZliongCi. ADAPTIVE QUADRILATERAL AND HEXAHEDRAL FINITE ELEMENT METHODS WITH HANGING NODES AND CONVERGENCE ANALYSIS. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2010, 28(5): 621-644, http://lib.cqvip.com/Qikan/Article/Detail?id=35211950.
[46] Zhao, Xuying, Mao, Shipeng, Shi, Zhongci. ADAPTIVE FINITE ELEMENT METHODS ON QUADRILATERAL MESHES WITHOUT HANGING NODES. SIAM JOURNAL ON SCIENTIFIC COMPUTING[J]. 2010, 32(4): 2099-2120, [47] Mao, Shipeng, Shi, Zhongci. High accuracy analysis of two nonconforming plate elements. NUMERISCHE MATHEMATIK[J]. 2009, 111(3): 407-443, https://www.webofscience.com/wos/woscc/full-record/WOS:000262281800005.
[48] 毛士鹏. Error estimates of triangular finite elements satisfy a weak angle condition. J. Comput. Appl. Math.. 2009, [49] Mao, Shipeng, Shi, Zhongci. EXPLICIT ERROR ESTIMATES FOR MIXED AND NONCONFORMING FINITE ELEMENTS. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2009, 27(4): 425-440, http://lib.cqvip.com/Qikan/Article/Detail?id=31072973.
[50] Shipeng Mao Zhong-ci Shi. EXPLICIT ERROR ESTIMATES FOR MIXED AND NONCONFORMING FINITE ELEMENTS. 计算数学：英文版. 2009, 425-440, http://lib.cqvip.com/Qikan/Article/Detail?id=31072973.
[51] Mao, Shipeng, Shi, Zhongci. Error estimates of triangular finite elements under a weak angle condition. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2009, 230(1): 329-331, https://www.webofscience.com/wos/woscc/full-record/WOS:000267237500029.
[52] Chen, Shaochun, Yang, Yongqin, Mao, Shipeng. Anisotropic conforming rectangular elements for elliptic problems of any order. APPLIED NUMERICAL MATHEMATICS[J]. 2009, 59(5): 1137-1148, https://www.webofscience.com/wos/woscc/full-record/WOS:000264925900019.
[53] 毛士鹏. On the interpolation error estimates for $Q_1$ quadrilateral finite elements. SIAM J. Numer. Anal.. 2009, [54] Becker, Roland, Mao, Shipeng. CONVERGENCE AND QUASI-OPTIMAL COMPLEXITY OF A SIMPLE ADAPTIVE FINITE ELEMENT METHOD. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE[J]. 2009, 43(6): 1203-1219, [55] Mao, Shipeng, Nicaise, Serge, Shi, ZhongCi. ON THE INTERPOLATION ERROR ESTIMATES FOR Q(1) QUADRILATERAL FINITE ELEMENTS. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2008, 47(1): 467-486, https://www.webofscience.com/wos/woscc/full-record/WOS:000263103800022.
[56] Becker, Roland, Mao, Shipeng, Shi, ZhongCi. A CONVERGENT ADAPTIVE FINITE ELEMENT METHOD WITH OPTIMAL COMPLEXITY. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS[J]. 2008, 30: 291-304, https://www.webofscience.com/wos/woscc/full-record/WOS:000267828900018.
[57] 毛士鹏. 各向异性有限元的理论及其应用. 2008, [58] Chen, Shaochun, Yin, Li, Mao, Shipeng. An anisotropic, superconvergent nonconforming plate finite element. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2008, 220(1-2): 96-110, https://www.webofscience.com/wos/woscc/full-record/WOS:000258636800011.
[59] Becker, Roland, Mao, Shipeng. An optimally convergent adaptive mixed finite element method. NUMERISCHE MATHEMATIK[J]. 2008, 111(1): 35-54, https://www.webofscience.com/wos/woscc/full-record/WOS:000260184800002.
[60] Rol. A convergent adaptive finite element method with optimal complexity. Kent State University * Institute of Computational Mathematics. 2008, http://oa.las.ac.cn/oainone/service/browseall/read1?ptype=JA&workid=JA201902013538264ZK.
[61] 毛士鹏. A quadrilateral nonconforming locking-free finite element method for the elasticity problem. Adv. Comput. Math.. 2008, [62] D. Shi, Shipeng Mao, S. Chen. A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM. 数学物理学报：B辑英文版[J]. 2007, 27(1): 193-202, http://lib.cqvip.com/Qikan/Article/Detail?id=23943063.
[63] Mao, Shipeng, Chen, Shaochun, Shi, Dongyang. Convergence and superconvergence of a nonconforming finite element on anisotropic meshes. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING[J]. 2007, 4(1): 16-38, https://www.webofscience.com/wos/woscc/full-record/WOS:000242811300002.
[64] Mao S P, Chen S. Convergence and superconvergence of a nonconforming finite element method for the Stokes problem. Journal of Numerical Mathematics[J]. 2006, [65] Dongyang Shi, Shipeng Mao, Hui Liang. Anisotropic Biquadratic Element with Superclose Result. Journal of Systems Science and Complexity[J]. 2006, 19(4): 566-576, [66] Mao, SP, Chen, SC. Accuracy analysis of Adini's non-conforming plate element on anisotropic meshes. COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING[J]. 2006, 22(5): 433-440, [67] Mao, SP, Chen, SC, Sun, HX. A quadrilateral, anisotropic, superconvergent, nonconforming double set parameter element. APPLIED NUMERICAL MATHEMATICS[J]. 2006, 56(7): 937-961, https://www.webofscience.com/wos/woscc/full-record/WOS:000237834500003.
[68] 毛士鹏. Analysis of an anisotropic nonconforming mixed finite element for 3D Stokes problem. Acta Math. Appl. Sin. 2006, [69] Shaochun Chen Huixia Sun Shipeng Mao. Anisotropic Superconvergence Analysis for the Wilson Nonconforming Element. 高等学校计算数学学报：英文版. 2006, 15(2): 180-192, http://lib.cqvip.com/Qikan/Article/Detail?id=21978026.
[70] Mao Shipeng, Shi Zhongci. Nonconforming rotated Q(1) element on non-tensor product anisotropic meshes. SCIENCE IN CHINA SERIES A-MATHEMATICS[J]. 2006, 49(10): 1363-1375, http://ir.amss.ac.cn/handle/2S8OKBNM/41727, http://www.irgrid.ac.cn/handle/1471x/6871046, http://ir.amss.ac.cn/handle/2S8OKBNM/41728.
[71] Mao, SP, Chen, SC. Convergence analysis of Morley element on anisotropic meshes. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2006, 24(2): 169-180, https://www.webofscience.com/wos/woscc/full-record/WOS:000235901100006.
[72] 毛士鹏, 石钟慈. 各向异性非内积型网格下旋转Q1元的收敛性. 中国科学(A辑:数学)[J]. 2006, 853-, http://ir.amss.ac.cn/handle/2S8OKBNM/46175, http://www.irgrid.ac.cn/handle/1471x/6871135, http://ir.amss.ac.cn/handle/2S8OKBNM/46176.
[73] Shi, DY, Mao, SP, Chen, SC. On the anisotropic accuracy analysis of ACM's nonconforming finite element. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2005, 23(6): 635-646, https://www.webofscience.com/wos/woscc/full-record/WOS:000234088400005.
[74] Dong-yangShi Shi-pengMao Shao-chunChen. AN ANISOTROPIC NONCONFORMING FINITE ELEMENT WITH SOME SUPERCONVERGENCE RESULTS. 计算数学：英文版. 2005, 23(3): 261-274, http://lib.cqvip.com/Qikan/Article/Detail?id=15991121.
[75] Shipeng Mao. Convergence analysis of the rotated Q1 element on anisotropic rectangular meshes. Kent State University * Institute of Computational Mathematics. 2005, http://oa.las.ac.cn/oainone/service/browseall/read1?ptype=JA&workid=JA201902014026751ZK.

（ 1 ） 自适应有限元方法的收敛性及其误差估计, 主持, 国家级, 2012-01--2014-12
（ 2 ） 重大研究计划：面向千万亿次计算的可扩展新型有限元算法及大规模并行程序, 参与, 国家级, 2012-01--2015-12
（ 3 ） 三维磁流体力学的高效自适应有限元方法, 主持, 国家级, 2015-01--2018-12
（ 4 ） 科技部国家重点研发计划：国家磁约束核聚变能发展研究专项(ITER), 参与, 国家级, 2015-01--2019-12
（ 5 ） 中国科学院青年创新促进会项目, 主持, 部委级, 2016-01--2019-12
（ 6 ） 科技部国家重点研发计划：E级高性能应用软件编程框架研制及应用示范, 参与, 国家级, 2016-07--2020-12
（ 7 ） 基于磁变量磁流体方程组的有限元方法研究, 主持, 国家级, 2019-01--2022-12
（ 8 ） 工信部工业创新发展工程重大项目: 基于工业平台的建模仿真引擎, 参与, 国家级, 2020-01--2022-12

（ 9 ） 可压缩湍流多重分形与统计特性的理论和数值研究,, 参与, 国家级, 2021-10--2024-12

 (10 ) 磁扩散方程高精度算法研究及MHD模块研制, 主持, 部委级, 2022-06--2024-6