偏微分方程数值解

有限元方法

控制与优化

形状与拓扑优化

数据同化

计算数学专业：硕士和博士研究生

070102-计算数学

偏微分方程数值解，控制与优化
形状与拓扑优化

2006-09--2009-07   中国科学院数学与系统科学研究院   理学博士
2003-09--2006-07   郑州大学数学系   理学硕士
1999-09--2003-07   郑州大学数学系   理学学士

2017.03--至今         中国科学院数学与系统科学研究院  副研究员

2009.07--2017.02   中国科学院数学与系统科学研究院 助理研究员

2010.09--2012.05   德国汉堡大学数学系  洪堡学者

2017-03~现在, 中国科学院数学与系统科学研究院, 副研究员
2014-06~2014-07,香港浸会大学数学系, 访问学者
2010-05~2012-05,德国汉堡大学数学系, 洪堡学者、博士后
2009-07~2017-02,中国科学院数学与系统科学研究院, 助理研究员

2024-01-01-今,数值计算与计算机应用, 编委
2022-04-30-今,Computational and Applied Mathematics, Associate Editor

偏微分方程约束优化的计算方法
微积分II-B习题课
微积分I-B习题课
微积分II习题课-B04-1
微积分I习题-B04-2

   

（1） 中国科学院数学与系统科学研究院2022年度科研进展, 研究所（学校）, 2022
（2） 中国科学院数学与系统科学研究院陈景润之星, 其他, 2017
（3） 洪堡学者, , 其他, 2010

[1] 李学建, 何晓明, 龚伟, Craig Douglas. Variational data assimilation with finite element discretization for second order parabolic interface equation. IMA Journal of Numerical Analysis[J]. 2024, 第 3 作者
[2] Gong, Wei, Li, Buyang, Rao, Qiqi. Convergent evolving finite element approximations of boundary evolution under shape gradient flow. IMA JOURNAL OF NUMERICAL ANALYSIS. 2023, 第 1 作者  通讯作者  http://dx.doi.org/10.1093/imanum/drad080.
[3] 李学建, 龚伟, 何晓明, 林涛. Variational data assimilation and its decoupled iterative numerical algorithms for Stokes-Darcy model. SIAM Journal on Scientific Computing[J]. 2023, 第 2 作者
[4] Gong, Wei, Liang, Dongdong, Xie, Xiaoping. Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains. ADVANCES IN COMPUTATIONAL MATHEMATICS[J]. 2023, 第 1 作者  通讯作者  49(2): http://dx.doi.org/10.1007/s10444-023-10017-3.
[5] Chen, Gang, Gong, Wei, Mateos, Mariano, Singler, John R, Zhang, Yangwen. A new global divergence free and pressure-robust HDG method for tangential boundary control of Stokes equations. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING[J]. 2023, 第 2 作者405: http://dx.doi.org/10.1016/j.cma.2022.115837.
[6] 龚伟, 李嘉杰, 朱升峰. Improved discrete boundary type shape gradients for PDE-constrained shape optimization. SIAM Journal on Scientific Computing[J]. 2022, 第 1 作者
[7] 常利利, 龚伟, 靳祯, 孙桂全. Sparse optimal control of pattern formations for an SIR reaction-diffusion epidemic model. SIAM Journal on Applied Mathematics[J]. 2022, 第 2 作者82(5): 1764-1790, 
[8] 龚伟, Zhiyu Tan, 周兆杰. Optimal convergence of finite element approximation to an optimization problem with PDE constraint. INVERSE PROBLEMS[J]. 2022, 第 1 作者
[9] 龚伟, Mariano Mateos, John R. Singler, Yangwen Zhang. Analysis and approximations of Dirichlet boundary control of Stokes flows in the energy space. SIAM Journal on Numerical Analysis[J]. 2022, 第 1 作者
[10] 周凯烨, 龚伟. Error estimates for finite element approximation of Dirichlet boundary control for Stokes equations in L^2(Gamma). Journal of Scientific Computing[J]. 2022, 第 2 作者  通讯作者  
[11] 龚伟, 朱升峰. On discrete shape gradient of boundary type for PDE-constrained shape optimization. SIAM Journal on Numerical Analysis[J]. 2021, 第 1 作者
[12] Gong, Wei, Hu, Weiwei, Mateos, Mariano, Singler, John R, Zhang, Yangwen. Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE[J]. 2020, 第 1 作者54(6): 2229-2264, https://www.webofscience.com/wos/woscc/full-record/WOS:000585906800003.
[13] Gong, Wei, Li, Buyang. Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems. IMA JOURNAL OF NUMERICAL ANALYSIS[J]. 2020, 第 1 作者40(4): 2898-2939, https://www.webofscience.com/wos/woscc/full-record/WOS:000610489200025.
[14] Gong, Wei, Liu, Wenbin, Tan, Zhiyu, Yan, Ningning. A convergent adaptive finite element method for elliptic Dirichlet boundary control problems. IMA JOURNAL OF NUMERICAL ANALYSIS[J]. 2019, 第 1 作者  通讯作者  39(4): 1985-2015, http://ir.amss.ac.cn/handle/2S8OKBNM/35974, http://www.irgrid.ac.cn/handle/1471x/6869840, http://ir.amss.ac.cn/handle/2S8OKBNM/35975, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000491253300013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=3a85505900f77cc629623c3f2907beab.
[15] Gong, Wei, Liu, Huipo, Yan, Ningning. Adaptive finite element method for parabolic equations with Dirac measure. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING[J]. 2018, 第 1 作者  通讯作者  328: 217-241, http://dx.doi.org/10.1016/j.cma.2017.08.051.
[16] Gong, Wei, Hu, Weiwei, Mateos, Mariano, Singler, John, Zhang, Xiao, Zhang, Yangwen. A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2018, 第 1 作者56(4): 2262-2287, https://www.webofscience.com/wos/woscc/full-record/WOS:000443291900012.
[17] Gong, Wei, Tan, Zhiyu, Zhang, Shuo. A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS[J]. 2018, 第 1 作者25(1): https://www.webofscience.com/wos/woscc/full-record/WOS:000417585300008.
[18] Gong, Wei, Xie, Hehu, Yan, Ningning. Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2017, 第 1 作者  通讯作者  72(2): 820-841, https://www.webofscience.com/wos/woscc/full-record/WOS:000406014800015.
[19] Gong, Wei, Yan, Ningning. Adaptive finite element method for elliptic optimal control problems: convergence and optimality. NUMERISCHE MATHEMATIK[J]. 2017, 第 1 作者  通讯作者  135(4): 1121-1170, https://www.webofscience.com/wos/woscc/full-record/WOS:000398175500006.
[20] Gong, Wei, Yan, Ningning. FINITE ELEMENT APPROXIMATIONS OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2016, 第 1 作者  通讯作者  54(2): 1229-1262, https://www.webofscience.com/wos/woscc/full-record/WOS:000375488100029.
[21] Gong, Wei, Hinze, Michael, Zhou, Zhaojie. Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2016, 第 1 作者  通讯作者  66(3): 941-967, https://www.webofscience.com/wos/woscc/full-record/WOS:000369911500003.
[22] Chang, Lili, Gong, Wei, Yan, Ningning. Numerical analysis for the approximation of optimal control problems with pointwise observations. MATHEMATICAL METHODS IN THE APPLIED SCIENCES[J]. 2015, 第 2 作者38(18): 4502-4520, https://www.webofscience.com/wos/woscc/full-record/WOS:000368252300005.
[23] Yan, Ming, Gong, Wei, Yan, Ningning. Finite element methods for elliptic optimal control problems with boundary observations. APPLIED NUMERICAL MATHEMATICS[J]. 2015, 第 2 作者90: 190-207, 
[24] Chang, Lili, Gong, Wei, Sun, Guiquan, Yan, Ningning. PDE-CONSTRAINED OPTIMAL CONTROL APPROACH FOR THE APPROXIMATION OF AN INVERSE CAUCHY PROBLEM. INVERSE PROBLEMS AND IMAGING[J]. 2015, 第 2 作者9(3): 791-814, https://www.webofscience.com/wos/woscc/full-record/WOS:000360672300008.
[25] Gong, Wei, Xie, Hehu, Yan, Ningning. A multilevel correction method for optimal controls of elliptic equation. SIAM Journal on Scientific Computing[J]. 2015, 第 1 作者http://arxiv.org/abs/1410.1132.
[26] Gong, Wei, Wang, Gengsheng, Yan, Ningning. APPROXIMATIONS OF ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD. SIAM JOURNAL ON CONTROL AND OPTIMIZATION[J]. 2014, 第 1 作者  通讯作者  52(3): 2008-2035, https://www.webofscience.com/wos/woscc/full-record/WOS:000338832300024.
[27] Gong, Wei, Hinze, Michael, Zhou, Zhaojie. A PRIORI ERROR ANALYSIS FOR FINITE ELEMENT APPROXIMATION OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH POINTWISE CONTROL. SIAM JOURNAL ON CONTROL AND OPTIMIZATION[J]. 2014, 第 1 作者  通讯作者  52(1): 97-119, https://www.webofscience.com/wos/woscc/full-record/WOS:000333536500005.
[28] Gong, Wei. ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF PARABOLIC EQUATIONS WITH MEASURE DATA. MATHEMATICS OF COMPUTATION[J]. 2013, 第 1 作者  通讯作者  82(281): 69-98, https://www.webofscience.com/wos/woscc/full-record/WOS:000326285800004.
[29] Gong, Wei, Hinze, Michael. Error estimates for parabolic optimal control problems with control and state constraints. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS[J]. 2013, 第 1 作者  通讯作者  56(1): 131-151, https://www.webofscience.com/wos/woscc/full-record/WOS:000321590500007.
[30] Gong, W, Hinze, M, Zhou, Z J. Space-time finite element approximation of parabolic optimal control problems. JOURNAL OF NUMERICAL MATHEMATICS[J]. 2012, 20(2): 111-145, http://dx.doi.org/10.1515/jnum-2012-0005.
[31] Gong, Wei, Yan, Ningning. A Mixed Finite Element Scheme for Optimal Control Problems with Pointwise State Constraints. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2011, 第 1 作者  通讯作者  46(2): 182-203, https://www.webofscience.com/wos/woscc/full-record/WOS:000286004700003.
[32] Gong, Wei, Yan, Ningning. MIXED FINITE ELEMENT METHOD FOR DIRICHLET BOUNDARY CONTROL PROBLEM GOVERNED BY ELLIPTIC PDES. SIAM JOURNAL ON CONTROL AND OPTIMIZATION[J]. 2011, 第 1 作者  通讯作者  49(3): 984-1014, https://www.webofscience.com/wos/woscc/full-record/WOS:000291870400004.
[33] Liu, Wenbin, Gong, Wei, Yan, Ningning. A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2009, 第 2 作者27(1): 97-114, http://lib.cqvip.com/Qikan/Article/Detail?id=29545477.
[34] 龚伟, 严宁宁. A posteriori error estimates for boundary control problems governed by the parabolic partial differential equations. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2009, 第 1 作者
[35] Gong, Wei, Li, Ruo, Yan, Ningning, Zhao, Weibo. An improved error analysis for finite element approximation of bioluminescence tomography. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2008, 第 1 作者26(3): 297-309, http://lib.cqvip.com/Qikan/Article/Detail?id=27610926.

   

（ 1 ） 状态受限最优控制问题的数值方法, 负责人, 国家任务, 2013-01--2015-12
（ 2 ） 两类偏微分方程最优控制问题的有限元方法, 负责人, 国家任务, 2014-01--2016-12
（ 3 ） 基于子空间方法的四维变分耦合同化系统及其在气候预测中的应用, 参与, 国家任务, 2014-01--2014-12
（ 4 ） 空间合作目标运动再现中跨尺度控制的前沿数学问题, 参与, 国家任务, 2012-09--2016-08
（ 5 ） 集合四维变分耦合同化的非线性子空间方法研究及其在年代际气候预测中的应用, 参与, 国家任务, 2016-01--2018-12
（ 6 ） 偏微分方程约束最优控制问题的区域分解方法, 负责人, 国家任务, 2017-01--2020-12
（ 7 ） 国家材料基因工程数据汇交与管理服务技术平台, 参与, 国家任务, 2018-07--2022-06
（ 8 ） 类地行星的形成演化及其宜居性, 参与, 中国科学院计划, 2020-01--2024-12
（ 9 ） 偏微分方程Dirichlet边界最优控制问题的理论与算法, 负责人, 国家任务, 2021-01--2024-12
（ 10 ） 近海工程及生态环境的数学建模和大规模高效模拟, 参与, 国家任务, 2022-11--2027-10

（1）PDE-constrained shape optimization: shape gradients, convergence and well-posedness   2024-06-29
（2）PDE-constrained shape optimization: shape gradients, convergence and well-posedness   第11届全国有限元会议   2023-09-23
（3）Dirichlet Boundary control of Stokes Equations in Polygonal Domain   2018-12-20
（4）Approximations of Tangential Boundary Control of Stokes Equations   2018-12-14

已指导学生

沈玥  博士研究生  070102-计算数学  

现指导学生

刘乐  硕士研究生  070102-计算数学  

周凯烨  博士研究生  070102-计算数学  

张紫翊  硕士研究生  070102-计算数学  

陶雪霖  博士研究生  070102-计算数学