1. hp有限元方法及其应用；

2. 谱方法及其应用；

3. 常微分、积分微分和时滞微分方程的高精度数值方法；

4. 偏微分方程时间方向的高精度方法;

5. 有限元方法的超收敛及后处理.

个人简介

易利军，教授，博士生导师。2004年和2007年于湖南师范大学数学系分别获得学士和硕士学位，2010年于上海师范大学计算数学专业获得博士学位。加拿大曼尼托巴大学(2014-2015)和新加坡南洋理工大学（2018）访问学者。主持4项国家级自然科学基金项目（含2项面上）、教育部博士点基金和上海市自然科学基金等资助项目；在计算数学和应用数学领域的顶级期刊《SIAM J. Numer. Anal.》、《Math. Comp.》和《Math. Models Methods Appl. Sci.》等发表SCI论文40余篇；担任美国《数学评论》和德国《数学文摘》评论员、国家自然科学基金和上海市科技奖励通讯评审专家等。

招生信息：

每年度招收计算数学专业博士生1-2名；计算数学专业硕士生2-3名，欢迎优秀的同学报考！

注：毕业研究生中5人获评“上海市优秀毕业生”；指导研究生以第一作者身份发表SCI论文近20篇；累计9人次获研究生国家奖学金。

工作经历

2020.9-至今，  上海师范大学数学系，教授

2014.9-2020.8  上海师范大学数学系，副教授

2014.9-2015.9  University of Manitoba, Canada, Visiting researcher

2010.7-2014.8  上海师范大学数学系，讲师 

教育经历

2007.9-2010.6  上海师范大学，计算数学专业，博士

2004.9-2007.6  湖南师范大学，基础数学专业，硕士  

2000.9-2004.6  湖南师范大学，数学与应用数学专业，学士

待发表论文

49. Benqi Guo and Lijun Yi*, Local Chebyshev operator and application to the h-p version of the finite element method for problems with nonhomogeneous Dirichlet boundary conditions, preprint.

48. Qunying Tu, Zhe Li and Lijun Yi*, Postprocessing technique of the discontinuous Galerkin method for solving delay differential equations, submitted.

47. Zhe Li, Qunying Tu and Lijun Yi*, A superconvergent postprocessing technique for the continuous Galerkin method in solving delay differential equations with nonlinear vanishing delay, submitted.

发表论文(*为通讯)

46. Zhe Li, Tao Sun and Lijun Yi*, Postprocessing-based a posteriori error estimation for spectral Galerkin approximations of fourth-order boundary value problems, East Asian Journal on Applied Mathematics, to appear.

45. Lina Wang, Mingzhu Zhang, Hongjiong Tian and Lijun Yi*, hp-version C^1-continuous Petrov-Galerkin method for nonlinear second-order initial value problems with application to wave equations, IMA Journal of Numerical Analysis, Doi:10.1093/ imanum/drae036, 2024.

44. Ang Ge, Jinye Shen*, Lijun Yi, Space-time continuous and time discontinuous Galerkin schemes based on isogeometric analysis for nonlinear time-fractional partial differential equations, Journal of Computational Mathematics, Doi:10.4208/jcm.2308-m2023-0075, 2023.

43. Mingzhu Zhang and Lijun Yi*, Postprocessing techniques of high-order Galerkin approximations to nonlinear second-order initial value problems with applications to wave equations, Communications in Computational Physics, 35 (2024), 816-858. (This paper is dedicated to Professor Benqi Guo on the occasion of his 80th Birthday.)

42. Lina Wang, Qian Tong, Lijun Yi* and Mingzhu Zhang, Legendre-Gauss-Radau spectral collocation method for nonlinear second-order initial value problems with applications to wave equations, Journal of Computational Mathematics, 42 (2024), 217-247.

41. Yuanyuan Zha, Zhe Li and Lijun Yi*, Superconvergent postprocessing of the C^1-conforming finite element method for fourth-order boundary value problems, Applied Numerical Mathematics, 193 (2023), 67-82.

40. Mingzhu Zhang, Xinyu Mao and Lijun Yi*, Superconvergence and postprocessing of the continuous Galerkin method for nonlinear Volterra integro-differential equations, ESAIM: Mathematical Modelling and Numerical Analysis, 57 (2023), 671-691.

39. Lijun Yi*, Mingzhu Zhang and Xinyu Mao, Superconvergent postprocessing of the discontinuous Galerkin time stepping method for nonlinear Volterra integro-differential equations, Journal of Computational and Applied Mathematics, 427 (2023), Paper No. 115140.

38. Mingzhu Zhang and Lijun Yi*, Superconvergent postprocessing of the continuous Galerkin time stepping method for nonlinear initial value problems with application to parabolic problems, Journal of Scientific Computing, 94 (2023), Paper No. 31.

37. Wansheng Wang* and Lijun Yi, Delay-dependent elliptic reconstruction and optimal L^\infty(L^2) a posteriori error estimates for fully discrete delay parabolic problems, Mathematics of Computation,  91 (2022), 2609-2643.

36. Yanping Chen*, Lina Wang and Lijun Yi, Exponential convergence of hp-discontinuous Galerkin method for nonlinear Caputo fractional differential equations, Journal of Scientific Computing, 92 (2022), Paper No. 99, 27 pp. 

35. Lina Wang, Yichen Wei and Lijun Yi*, An a priori error analysis of the hp-version of the C^0-continuous Petrov-Galerkin method for nonlinear second-order delay differential equations, International Journal of Computer Mathematics,  99 (2022), 1557-1578.

34. Mingzhu Zhang, Xinyu Mao and Lijun Yi*, Exponential convergence of the hp-version of the composite Gauss-Legendre quadrature for integrals with endpoint singularities, Applied Numerical Mathematics, 170 (2021),340-352.

33. Lina Wang, Hongjiong Tian and Lijun Yi*,An h-p version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels, Applied Numerical Mathematics, 161 (2021) , 218-232.

32. Shuangshuang Li, Lina Wang and Lijun Yi*, An hp-version C^0-continuous Petrov-Galerkin time-stepping method for second-order Volterra integro-differential equations with weakly singular kernels, East Asian Journal on Applied Mathematics, 11 (2021), 20-42.

31. Yiyun Qian, YuanYuan Zha, Kangwen Cai, Yanqin Liu, Xinyi Wang, and Lijun Yi*, Superconvergence of spectral collocation method for initial value problem of ordinary differential equations (in Chinese), Journal of Shanghai Normal University (Natural Sciences), (50) 2021, 1‒7. (本科生大创项目成果)

30. Wansheng Wang*, Lijun Yi and Aiguo Xiao, A posteriori error estimates for fully discrete finite element method for generalized diffusion equation with delay, Journal of Scientific Computing,  84 (2020), Article No. 13, 27 pp. 

29. Lina Wang, Lijun Yi* and Hongli Jia, An h-p version of the Chebyshev spectral collocation method for Volterra integro-differential equations with vanishing delays, Journal of Integral Equations and Applications, (32)2020, 101-128.

28. Yichen Wei and Lijun Yi*, An hp-version of the C^0-continuous Galerkin time-stepping method for nonlinear second-order initial value problems,  Advances in Computational Mathematics,  46 (2020), Article No. 56, 25 pp.

27. Ling Guo and Lijun Yi*, A stochastic collocation method for Volterra integro-differential equations with weakly singular kernels and random inputs, International Journal for Uncertainty Quantification,  10 (2020), 129-143.

26. Shuangshuang Li, Lina Wang and Lijun Yi*, An hp-version of the C^0-continuous Petrov-Galerkin method for second-order Volterra integro-differential equations, Applied Numerical Mathematics, 152 (2020), 84-104.

25. Yichen Wei, Tao Sun and Lijun Yi*,An h-p version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays, Journal of Computational and Applied Mathematics, 364(2020), 112348, 22pp.

24.Lina Wang and Lijun Yi*, An h-p version of the discontinuous Galerkin method for Volterra integro-differential equations with vanishing delays, Journal of Scientific Computing,  81 (2019), 2303-2330.

23. Jinghua Xie and Lijun Yi*, An h-p version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations, Applied Numerical Mathematics, 143(2019), 1-19.

22. Tingting Meng, Zhongqing Wang and Lijun Yi*,  An h-p version of the Chebyshev spectral collocation method for nonlinear delay differential equations, Numerical Methods for Partial Differential Equations, 35 (2019), 664-680.

21. Lijun Yi and Benqi Guo*, The h-p version of the continuous Petrov-Galerkin method for nonlinear Volterra functional integro-differential equations with vanishing delays, International Journal of Numerical Analysis and Modeling, 15 (2018), 26-47.

20. Tingting Meng and Lijun Yi*, An h-p version of thecontinuous Petrov-Galerkin method for nonlinear delay differential equations，Journal of Scientific Computing, 74 (2018), 1091-1114.

19. Lina Wang and Lijun Yi*, An h-p version of thecontinuous Petrov-Galerkin method for Volterra delay-integro-differential equations，Advances in Computational Mathematics, 43 (2017), 1437-1467.

18. Zhongqing Wang*, Yuling Guo and Lijun Yi, An hp-version Legendre-Jacobi spectral collocation method for Volterra integro-differential equations with smooth and weakly singular kernels,Mathematics of Computation, 86 (2017), 2285–2324.

17. Lijun Yi and Zhongqing Wang*, A Legendre-Gauss-Radau spectral collocation method for firstorder nonlinear delay differential equations,Calcolo, 53 (2016),691-721.

16. Tao Sun* and Lijun Yi, A new Galerkin spectral element method for fourth-order boundary value problems, International Journal of Computer Mathematics, 93 (2016), 915-928.

15. LijunYi* and Benqi Guo, An h-p version of the continuous Petrov-Galerkin finite element method for Volterra integro-differential equations with smooth andnon-smooth kernels, SIAM Journal on Numerical Analysis, 53 (2015), 2677-2704.

14. LijunYi*, An L^infty-error estimate for the h-p version continuous Petrov-Galerkin method for nonlinear initial value problems, East Asian Journal on Applied Mathematics, 5(2015), 301-311.

13. LijunYi*, An h-p version of the continuous Petrov-Galerkin finite element method for nonlinear Volterra integro-differential equations, Journal of Scientific Computing, 65 (2015),715-734.  (This paper is dedicated to Professor Benqi Guo on the occasion of his 70th Birthday.)

12. LijunYi* and Benqi Guo, An h-p Petrov-Galerkin finite element method for linear Volterra integro-differential equations, Science China Mathematics, 57 (2014),2285-2300.

11. Tao Sun and Lijun Yi*, A Petrov-Galerkin Spectral Method for Fourth-Order Problems, Mathematical Methods in the Applied Sciences, 37 (2014), 2257-2270.

10. Lijun Yi and Zhongqing Wang*, Legendre-Gauss-type collocation algorithms for nonlinear ordinary/ partial differential equations, International Journal of Computer Mathematics, 91 (2014), 1434-1460.

9. Lijun Yi and Zhongqing Wang*, Legendre-Gauss spectral collocation method for second order nonlinear delay differential equations, Numerical Mathematics: Theory, Methods and Application, 7 (2014), 149-178.

8. Lijun Yi and Zhongqing Wang*, Legendre spectral collocation method for second order nonlinear ordinary/partial differential equations, Discrete and Continuous Dynamical Systems Series B, 19 (2014), 299-322.

7. Lijun Yi, Ziqiang Liang and Zhongqing Wang*, Legendre-Gauss-Lobatto spectral collocation method for nonlinear delay differential equations, Mathematical Methods in the Applied Sciences, 36 (2013) 2476-2491.

6. Benqi Guo* and Lijun Yi, Local Chebyshev projection-interpolation operator and application to the h-p version of the finite element method in three dimensions, Mathematical Models and Methods in Applied Sciences, 23(2013), 777-801.

5. Lingxiong Meng, Honghui Liang and Lijun Yi*, Recovery for finite element approximation of an eigenvalue problem under mixed mesh (in Chinese),  Communications on Applied Mathematics and Computation, 27 (2013), 33–39.

4. Tao Sun* and Lijun Yi, A Petrov-Galerkin spectral method for fourth-order mixed nonhomogeneous boundary value problems (in Chinese), Mathematics in Practice and Theory, 43 (2013), 255–260.

3. Lijun Yi*, On the asymptotic exactness of errorestimators based on the equilibrated residual method for quadrilateral finite elements, Applied Numerical Mathematics, 62 (2012), 1925-1937.

2. LijunYi and Benqi Guo*, A-posteriori error estimation for the Legendre spectral Galerkin method in one dimension, Numerical Mathematics: Theory, Methods and Application, 3 (2010),40-52.

1. LijunYi and Benqi Guo*, Superconvergence of the h-p version of the finite element method in one dimension, Journal of Computational and Applied Mathematics,233 (2009), 150-164.

主持项目

1.国家自然科学基金面上项目, 几类发展方程的hp型Galerkin时间步进法，No.12171322，2022.1-2025.12，在研.

2.国家自然科学基金面上项目，积分微分方程的hp时间步进法及其自适应算法，No.11771298，2018.1-2021.12，已结题.

3.国家自然科学基金青年基金，非线性发展方程的时空高精度谱配置算法，No. 11301343，2014.1-2016.12，已结题.

4.国家自然科学基金数学天元基金，非线性时滞微分方程的谱配置方法研究，No. 11226330，2013.1-2013.12，已结题.

5.教育部高校博士点基金，多面体区域上椭圆边值问题的h-p型有限元方法研究，No. 20113127120002，2012.1-2014.12，已结题. 

6.上海市自然科学基金, 具有记忆项的偏积分微分方程的时空高精度方法, No.21ZR1447200，2021.7-2024.6，在研.

7.上海高校青年教师培养资助计划资助项目, 多面体区域上h-p型有限元方法研究, No. shsf018, 2011.12-2014.6, 已结题. 

8.上海师范大学“原创与前瞻性预研项目”，非线性时滞积分微分方程的hp有限元方法，No.DYL201703， 2017.1-2018.12，已结题.

9.上海师范大学校一般科研项目，h-p型有限元方法的后验误差估计，No. SK201117，2011.1-2012.12，已结题.

指导的研究生

1. 王利娜，硕士，2015.9-2018.6，在AiCM,JSC和JIEA发表SCI论文3篇；2016年获研究生数模竞赛全国三等奖；获2017年度“研究生国家奖学金”；“2018年度上海师范大学优秀毕业生”；博士(联合指导), 2019.9-2022.6,发表SCI论文5篇,“2022年度上海师范大学优秀毕业生”；毕业去向：河南工程学院.

2. 孟婷婷，硕士，2015.9-2018.6，在JSC和NMPDE发表SCI论文2篇；2017年获研究生数模竞赛全国三等奖；获2017年度“研究生国家奖学金”；“2018年度上海师范大学优秀毕业生”；毕业去向：上海华二紫竹双语学校.

3. 魏怿琛，硕士，2017.9-2020.6，在JCAM和AiCM发表SCI论文2篇；2018年获研究生数模竞赛全国一等奖；获2019年度“研究生国家奖学金”；“2020年度上海市优秀毕业生”；毕业去向：上海市进才中学北校.

4. 谢菁华，硕士，2017.9-2020.6，在ANM发表SCI论文1篇；2018年获研究生数模竞赛全国一等奖；获2019年度“研究生国家奖学金”；“2020年度上海市优秀毕业生”；毕业去向：上海市徐汇中学.

5. 李双双，硕士，2018.9-2021.6,在ANM和EAJAM发表SCI论文2篇; 2019年获研究生数模竞赛全国三等奖；获2020年度“研究生国家奖学金”;“2020年度上海市优秀毕业生”; 毕业去向：上海市南洋初级中学.

6. 佟 倩，硕士，2018.9-2021.6, 2019年获研究生数模竞赛全国三等奖，上海师范大学优秀学位论文奖; 毕业去向：上海古美高级中学.

7.毛新宇,硕士，2020.9-2023.6，以二作身份在ANM,JCAM和ESAIM:M2AN发表SCI论文3篇；2022年获研究生数模竞赛全国三等奖; 毕业去向：上海市南洋模范初级中学.

8. 张明珠，硕博连读，2020.9-至今...

9. 查媛媛，硕士，2021.9-至今...

10. 李 哲，硕士，2021.9-至今...

11. 贺高情，硕士，2022.9-至今...

12. 梁韵怡，硕士，2022.9-至今...

13. 涂群英，硕士，2022.9-至今...

14. 罗 婕，硕士，2023.9-至今...

1. 2018年度上海师范大学“教学优秀奖”，2018年11月.

2. 2018年度上海师范大学“精彩课堂”提名奖，2018年6月.

3. 第八届上海师范大学“优秀青年学术骨干”，2017年12月.

4. 第一届青年优秀论文二等奖，中国仿真学会仿真算法专业委员会，2017年8月.

1. 美国《Mathscinet》(数学评论)和德国《zbmath》(数学文摘)评论员

2. 国家自然科学基金及上海市科技奖励通讯评审专家

3. 中国工业与应用数学学会会员及中国仿真学会仿真算法专业委员会会员

4. 担任SINUM,SISC,JCP,AiCM,CiCP,JSC,ANM,M2AS和JCAM等多个SCI期刊的审稿人

Last updated on Feb. 2024.