趙衛東

趙衛東，山東大學數學學院博士生導師，1987年留校至今。

主要從事計算方法方面的工作。

1. 發展熱離子問題有限元解的收斂性分析 山東大學學報 29 1994.12.

2. 多孔介質二相可混溶不可壓縮驅動問題的特徵混合元方法的數值分析 海洋出版社 1994.

3. Navier-Stokes方程的特徵混合元方法的數值分析 山東大學學報 30 1995.3.

4, 多孔介質二相驅動問題壓力方程Galerkin方法后處理特徵方法的迭代解法次收斂性分析 全國油、水資源模擬及數值方法研討會論文集 1995.9.

5. 二維Burgers方程的一種新的修正特徵有限元方法 1995年計算數學鄭州會議論文集1995.10.

6. 油氣資源數值模擬系統的數值方法及軟體 CSIAM'96中國工業與應用數學學會第四次大會論文集

復旦大學出版社1996.7 與袁益讓、王文洽合作.

7. 熱敏電阻器模型問題的有限差分解法及其收斂性分析 第十屆全國水動力學學術會議論文集

海洋出版社1996.7.

8. 二維Burgers方程的一種修正特徵有限元方法及其收斂性分析 高科技研究中的數值計算(二)

科學與工程計算叢書編輯部1996.7.

9. 二維對流擴散問題的一種新的修正特徵有限元方法及其收斂性分析 第二屆全國海事技術研討會文集(下)

海洋出版社1996.5.

11. 多孔介質不混溶驅動問題的一種新的差分解法及收斂性分析 山東大學學報 Vol.32 1997.

12. 對流擴散方程特徵有限元的高階格式 第八屆全國高等學校計算數學會議論文集 1997 與程愛傑合作

13.多孔介質不混溶驅動問題的一種新的差分解法及收斂性分析 山東大學學報 Vol.32 1997.

14. Dong Liang and Weidong Zhao, A high-order upwind method for convection-diffusion problem, Comput. Method. Appl. Mech. Eng., 147(1-2), 1997, pp. 107-115.

15. Weidong Zhao, An iterative method and its convergent analysis of a new modified characteristic finite element method for miscible displacement in porous media, Numer. Math., 20(3), 1998, pp. 279-288.

16. Yirang Yuan, Weidong Zhao, Aijie Cheng and Yuji Han, Oil resources evaluating numerical simulation of migration-accumulation, the Fifth Meeting of ASIAM’98, Qinghua University Press, 1998.

17. Yirang Yuan, Weidong Zhao, The characteristic finite difference method for 3-dimensional moving boundary value problem, Numer. Math.-Engl., 7(2), 1998, pp.133-144.

18. Aijie Cheng and Weidong Zhao, Alternating direction finite difference method for convection-diffusion equation, J. Shandong Univ., 34(1), 1999, pp. 10-16.

19. Weidong Zhao, Splitting upwind finite difference method for convection-diffusion equation, the Sixth Annual Meeting of Mathematical Computation, Shanghai, China, 1999.

20. YirangYuan and Weidong Zhao, Characteristic finite difference method for 2-D seepageproblems of compressible oil and water with moving boundary, J. Sys. Sci. Math.Sci., 19(1), 1999, pp. 6-15.

21. DongLiang and Weidong Zhao, The weighted factor method for seepage problems,Developments of Water and Electric Engineering in China, Ocean Press, Beijing,1999.

22. WeidongZhao and Aijie Cheng, A kind of improved characteristic finite element methodfor convection-diffusion equation, Numer. Math., 21(3), 1999, pp. 248-263.

23. WeidongZhao, The finite difference method and its convergence analysis for thermistorproblem, Appli. Math., 14(3), 1999, pp. 349-358.

24. YirangYuan, Weidong Zhao, Aijie Cheng and Yuji Han, Simulation andapplication of three dimensional migration-accumulation of oil resources, Appl. Math. Mech.-Engl. 20(9), 1999, pp. 999-1009.

25. Yirang Yuan, Weidong Zhao, Aijie Cheng and Yuji Han, Numerical simulation analysis of migration-accumulation of oil and water, Appl. Math. Mech.-Engl. 20(4), 1999, pp. 406-412.

26. Weidong Zhao, A high-order upwind method for convection-diffusion equation with Newmann boundary condition, Numerical Treatment of Multiphase Flows in Porous Media, 552, 2000, pp. 430-440.

27. Yirang Yuan, Weidong Zhao, Aijie Cheng and Yuji Han, Numerical simulation of migration-accumulation for multi-layer oil resources and its application, the Sixth Meeting of ASIAM 2000, Qinghua University Press, 2000.

28. Aijie Cheng and Weidong Zhao, An economical difference scheme for convection-diffusion equation, Math. Numer. Sinica, 22(3), 2000, pp. 309-318.

29. Weidong Zhao, Characteristic method for two-phase displacement in porous media and its convergent analysis bg on the past-progressing of finite element method for pressure, J. Shandong Univ., 35(1), 2000, pp.1-7.

30. Weidong Zhao, A Class of improved characteristic finite element method for convection diffusion equation, International Conference on applied Computational Fluid Dynamics, Beijing, China, 2000, pp. 500-505.

31. Weidong Zhao, The mixed least-square and characteristic finite element method for two-phase displacement in porous media, Mathematica Numerica Sinica, 22(1), 2000, pp. 83-96.

32. Yirang Yuan, Weidong Zhao, Aijie Cheng, Wenqia Wang and Yuji Han, Numerical simulation of oil migration-accumulation of multilayer and its application, Appl. Math. Mech.-Engl., 23(8), 2002, pp. 931-941.

33. Hong Wang, Weidong Zhao, Rechard E. Ewing, Stephen L. Lyon and Guan Qin, An ELLAM simulator for highly compressible flow through porous media with multiple wells, Comtemp. Math., 295, 2002, pp. 481-488.

34. Hong Wang and Weidong Zhao, A modified alternating-direction finite volume method for the modeling of secondary hydrocarbon migration and accumulation processes, media with multiple wells, XIV International Conference on Computational Methods in Water Resources, Delft, Netherlands, 2, 2002, pp. 987-994.

35. Hong Wang, Weidong Zhao, Rechard E. Ewing, Stephen L. Lyon and Guan Qin, An ELLAM simulator for highly compressible flow through three-dimensional porous media with multiple wells, XIV International Conference on Computational Methods in Water Resources, Delft, Netherlands, 2, 2002, pp. 1051-1058.

36. Weidong Zhao and Dong Liang, Modified high-order method for convection diffusion equation, Acta Mathematicae Applicatae Sinica, 18(1), 2002, pp. 131-146.

37. Hong Wang and Weidong Zhao, A modified alternating-direction finite volume method for the modeling of secondary hydrocarbon migration and accumulation processes, Numer. Meth. Part. D. E., 19(2), 2003, pp. 245-270.

38. Hong Wang and Weidong Zhao, An upwind finite volume scheme and its maximum -principle-preserving ADI splitting for unsteady-state advection-diffusion equations, Numer. Meth. Part. D. E., 19(2), 2003, pp. 211-226.

39. Dong Liang and Weidong Zhao, The weighted upwinding finite volume method for the convection diffusion problem on a nonstandard covolume grid, Appl. Num. Anal. Comp. Math., 1(1), 2004, pp. 180-194.

40. Hong Wang, Weidong Zhao, Magne S. Espedal and Aleksey S. Telyakovskiyd, An Eulerian-Lagrangian localized adjoint method for compositional multiphase flow in the subsurface, Developments in Water Science, 55(1), 2004, pp. 495-504.

41. H. Wang, W. Zhao and R.E. Ewing, A numerical modeling of multicomponent compressible flows in porous media with multiple wells by a Eulerian-Lagrangian method, Comput. Visual. Sci., 8(2), 2005, pp. 69-81.

42. H. Wang, W. Zhao, R.E. Ewing, M. Al-Lawada, M.S. Espedal and A.S. telyakovskiy, An Eulerian-Lagrangian solution technique for single-phase compositional flow in three-dimensional porous media, Int. J. Comput. Math. Appl., 52(5), 2006, pp. 607-624.

43. D. Liang and W. Zhao, An optimal weighted upwinding covolume method on non-standard grids for convection-diffusion problems in 2D, Int. J. Numer. Meth. Eng., 67(4), 2006, pp. 553-577.

44. Lili Ju, Max Gunzburger and Weidong Zhao, Adaptive finite element methods for elliptic PDEs based on conforming centroidal voronoi–delaunay triangulations, SIAM J. Sci. Comput., 28(6), 2006, pp. 2023-2053. 45. Weidong Zhao, Lifeng Chen and Shige Peng, A new kind of accurate numerical methods for backward stochastic differential equations, SIAM J. Sci. Comput., 28(4), 2006, pp. 1563-1582.

46. Peng Sun and Weidong Zhao, Alternating direction upwind control volume method for Asian option pricing problems, J. Shandong Univ.,42(6), 2007, pp. 16-21.

47. Peng Sun, Lei Zhang and Weidong Zhao, One kind of finite control volume numerical method for American option problems, J. Shandong Univ., 42(6), 2007, pp. 1-6.

48. Yanzhao Cao, Hongmei Chi, C. Milton and Weidong Zhao, Exploitation of sensitivity derivatives via randomized quasi-Monte Carlo methods, Monte Carlo Methods Appl., 14(3), 2008, pp. 269-279.

49. Weidong Zhao, Li Tian and Lili Ju, Convergence analysis of a splitting method for stochastic differential equations, Int. J. Numer. Anal. Model., 5(4), 2008, pp. 673-692.

50. Lili Ju, Wensong Wu and Weidong Zhao, Adaptive finite volume methods for steady convection-diffusion equations with mesh optimization, Discrete Contin. Dyn. Syst. Ser. B, 11(3), 2009, pp. 669-690.

51. Jinlei Wang, Shenxi Luo and Weidong Zhao, Crank-Nicolson scheme and its error estimates for backward stochastic differential equations, Acta Mathematicae Applicatae Sinica, English Series, 2009.

52. Weidong Zhao, Jinlei Wang and Shige Peng, Error estimates of the $\theta$-scheme for backward stochastic differential equations, Discrete Contin. Dyn. Syst. Ser. B, 12(4), 2009, pp. 905-924.

53. Yanzhao Cao, Max Gunzburger, X. B. Hu, Fei Hua, Xiaoming Wang, and Weidong Zhao, Finite element approximations for Stokes-Darcy flow with Beaver-Joseph interface conditions, SIAM J. Numer. Anal., 47(6), 2010, pp. 4239-4256.

54. Yang Li and Weidong Zhao, L^p-error estimates for numerical schemes for solving certain kinds of backward stochastic differential equations, Statistics and Probability Letters, 80(21-22), 2010, pp.1612-1617.

55. Weidong Zhao, Guannan Zhang, and Lili Ju, A stable multistep scheme for solving backward stochastic differential equations, SIAM J. Numer. Anal., 48(4), 2010, pp. 1369-1394.

56. Guangbao Guo and Weidong Zhao, Schwarz methods for quasi stationary distributions of Markov chains, Calcolo March, 49(1), 2012, pp. 21-39.

57. Yang Li and Weidong Zhao, Error estimates of a second order numerical scheme for a kind of backward stochastic differential equations, 2011 World Congress on Engineering and Technology, Oct. 28-Nov. 2, 2011, Shanghai, China.

58. Feng Bao, Yanzhao Cao and Weidong Zhao, Numerical solutions for forward backward doubly stochastic differential equations and Zakai equations, International Journal for Uncertainty Quantification, 1(4), 2011, pp. 351–367.

59. Weidong Zhao, Yang Li and Guannan Zhang, A generalized θ-scheme for solving backward stochastic differential equations, Discrete Contin. Dyn. Syst. Ser. B, 17(5), 2012, pp.1585-1603.

60. Lili Ju, Li Tian, Xiao Xiao and Weidong Zhao, Covolume-upwind finite volume approximations for linear elliptic partial differential equations, J. Comput. Phys., 231(18), 2012, pp. 6097-6120.

61. Guannan Zhang, Max Gunzburger and Weidong Zhao, A sparse-grid method for multi-dimensional backward stochastic differential equations, J. Comput. Math., 31(3), 2013, pp. 221-248.

62. Hong Wang, Weidong Zhao , Magne S. Espedal and Aleksey S.Telyakovskiy, A component-based Eulerian--Lagrangian formulation for multicomponent multiphase compositional flow and transport in porous media, SIAM J. Sci. Comput., 35(2), 2013, pp. B462-B486.

63. Weidong Zhao, Yang Li and Lili Ju, Error estimates of the Crank-Nicolson scheme for solving backward stochastic differential equations, Int. J. Numer. Anal. Model., 10(4), 2013, pp. 876-898.

64. Weidong Zhao, Yang Li and Yu Fu, Second-order schemes for solving decoupled forward backward stochastic differential equations, Sci. China Math., 57(4), 2014, 665-686.

65. Weidong Zhao, Wei Zhang and Lili Ju, A numerical method and its error estimates for the decoupled forward-backward stochastic differential equations, Commun. Comput. Phys., 15(3), 2014, pp. 618-646.

66. Weidong Zhao, Yu Fu and Tao Zhou, New kinds of high-order multistep schemes for coupled forward backward stochastic differential equations, SIAM J. Sci. Comput., 36(4), 2014, pp. A1731–A1751.

67. Yu Fu and Weidong Zhao, An explicit second-order numerical scheme to solve decoupled forward backward stochastic equations, East Asian J. Appl. Math., 4(4), 2014, pp. 368-385.

68. Wei Zhang and Weidong Zhao, Euler-type schemes for weakly coupled FBSDEs and the optimal convergence analysis, Front. Math. China, 10(2), 2015, pp. 415-434.

69. Feng Bao, Yanzhao Cao and Weidong Zhao, A first order semi-discrete algorithm for backward doubly stochastic differential equations, Discrete Contin. Dyn. Syst. Ser. B, 20(5), 2015, pp.1297-1313.

70. Jie Yang and Weidong Zhao, Convergence analysis of a class of multistep schemes for forward-backward stochastic differential equations, East Asian J. Appl. Math., 5(4), 2015, pp. 387-404.

71. Tao Kong, Weidong Zhao and Tao Zhou, Probabilistic high order numerical schemes for fully nonlinear parabolic PDEs, Commun. Comput. Phys., 18(5), 2015, pp. 1482-1503.

72. Liyong Zhu, Lili Ju and Weidong Zhao, Fast high-order compact exponential time differencing Runge-Kutta methods for second-order semilinear parabolic equations, J. Sci. Comput., 67(3), 2016, pp. 1043-1065.

73. 趙衛東，正倒向隨機微分方程組的數值解法，計算數學，37(4), 2015, pp. 1-37.

74. Xu Yang and Weidong Zhao, Strong convergence analysis of split-step $\theta$-method for nonlinear stochastic differential equations with jumps, Adv. Appl. Math. Mech., 8(6), 2016, pp. 1004-1022.

75. Feng Bao, Yanzhao Cao, Amnon Meir and Weidong Zhao, A first Order Scheme for Backward Doubly Stochastic Differential Equations, SIAM/ASA J. Uncertain. Quan., 4, 2016, pp. 413-445.

76. Guannan Zhang, Weidong Zhao, Clayton Webster and Max Gunzburger, Numerical methods for a class of nonlocal diffusion problems with the use of backward SDEs, Comput. Math. Appl., 71(11), 2016, pp. 2479-2496.

77. Weidong Zhao, Wei Zhang and Lili Ju, A multistep scheme for decoupled forward-backward stochastic differential equations, Numer. Math. Theory Methods Appl., 9(2), 2016, pp. 262-288.

78. Yu Fu, Weidong Zhao and Tao Zhou, Multistep schemes for forward backward stochastic differential equations with jumps, J. Sci. Comput., 69(2), 2016, pp. 651-672.

79. Jie Yang and Weidong Zhao, Numerical simulations of the G-Brownian motion, Front. Math. China, 11(6), 2016, pp. 1625-1643.

80. Yu Fu, Jie Yang and Weidong Zhao, Prediction-correction scheme for decoupled forward backward stochastic differential equations with jumps, East Asian J. Appl. Math., 6(3), 2016, pp. 253-277.

81. BillX.Hu, YanzhaoCao, WeidongZhao and FengBao, Identification of hydraulic conductivity distributions in density dependent flow fields of submarine groundwater discharge modeling using adjoint-state sensitivities, Sci. China Earth Sci., 59(4), 2016, pp. 770-779.

82. Yang Li, Jie Yang and Weidong Zhao, Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs, Sci. China Math., 2016.

83. Weidong Zhao, Wei Zhang and Guannan Zhang, Second-order numerical schemes for decoupled forward-backward stochastic differential equations with jumps, J. Comput. Math., 2016.

84. Jie Yang, Guannan Zhang and Weidong Zhao, An accurate numerical scheme for forward-backward stochastic differential equations in bounded domains, J. Comput. Math., 2016.

個人主頁：

1 發展熱離子問題有限元解的收斂性分析 山東大學學報 29 1994.12。

2 多孔介質二相可混溶不可壓縮驅動問題的特徵混合元方法的數值分析 海洋出版社 1994。

3 Navier-Stokes方程的特徵混合元方法的數值分析 山東大學學報 30 1995.3。

4 多孔介質二相驅動問題壓力方程Galerkin方法后處理特徵方法的迭代解法次收斂性分析 全國油、水資源模擬及數值方法研討會論文集 1995.9。

5 二維Burgers方程的一種新的修正特徵有限元方法 1995年計算數學鄭州會議論文集。