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博士学位论文：不可压缩Navier-Stokes方程变分多尺度方法研究

 

1. Jiaping Yu, Haibiao Zheng*, Feng Shi. A finite element variational multiscale method for incompressible flows based on the construction of the projection basis functions. International Journal for Numerical Methods in Fluids, 2012, 70: 793-804 (SCI 008PE).

2. Haibiao Zheng*, Yanren Hou, Feng Shi, A posteriori error estimates of stabilization of low-order mixed finite elements for incompressible flow[J]. SIAM J. Sci. Comput., 2010, 32: 1346-1361 (SCI 608IE).

3. Haibiao Zheng*, Li Shan, Yanren Hou, A quadratic equal-order stabilized method for Stokes problem based on two local Gauss integrations[J]. Numerical Methods for Partial Differential Equations, 2010, 26: 1180-1190 (SCI 640NH).

4. Haibiao Zheng*, Yanren Hou, Feng Shi, Adaptive Variational multiscale methods for incompressible flow based on two local Gauss integrations[J]. Journal of Computational Physics, 2010, 229: 7030-7041 (SCI 646VG).

5. Haibiao Zheng*, Yanren Hou, Feng Shi, Lina Song, A finite element variational multiscale method for incompressible flows based on two local Gauss integrations[J].Journal of Computational Physics, 2009, 228: 5961-5971 (SCI 474PH).

6. Lina Song, Yanren Hou, Haibiao Zheng, Adaptive Local Postprocessing Finite Element Method for the Navier-Stokes Equations[J], J. Sci. Computing, 55(2013), 255-267.(SCI 131DS)

7. Li Shan, Yanren Hou, Haibiao Zheng*, Variational Multiscale method Based on the Crank-Nicolson Extrapolation scheme for the non-stationary Navier-Stokes equations, International Journal of Computer Mathematics, 2012, 89(16): 2198-2223. (SCI 042PG).

8. Li Shan, Haibiao Zheng, W.J. Layton, A decoupling method with different subdomain time steps for the nonstationary stokes-darcy model [J], Numer.Method for Partial Differential Equations, 2013, 29(2): 549-583.（SCI 076XZ）

9. Li Shan, W.J.Layton, Haibiao Zheng, Numerical analysis of modular VMS methods with nonlinear eddy viscosity for the Navier-Stokes equations, International Journal of Numerical Analysis and Modelling, 2013, 10(4): 943-971.（SCI 217IW ）

10. Lina Song, Yanren Hou, Haibiao Zheng, Adaptive variational multiscale Method for the Stokes equations[J], International Journal for Numerical Methods in Fluids, 2013, 71: 1369-1381.(SCI 112VT)

11. Haibiao Zheng, Jiaping Yu, Kaitai Li, Feng Shi, A variational multiscale method with bubble stabilization for the Oseen problem based on two local Gauss integrations[J], Applied Mathematics and Computation, 2012, 219(8): 3701-3708.(SCI 041WA).

12. Li Shan, Haibiao Zheng*, Partitioned time stepping method for fully evolutionary Stokes-Darcy flow with Beavers-Joseph interface conditions[J], SIAM J. Numer. Anal., 2013, 51(2): 813–839.(SCI 136ZZ)

13. Haibiao Zheng, Feng Shi, Yanren Hou,  Jianping Zhao. A new local and parallel finite element algorithm based on the partition of unity [J], submit to

14. Jiaping Yu,  Feng Shi, Haibiao Zheng. Local and parallel finite element method based on the partition of unity for the Stokes problem[J],  SIAM J. Sci. Comput., 2014, 36(5): C547-C567.http://dx.doi.org/10.1137/130925748

15. Haibiao Zheng, Jiaping Yu, Feng Shi. Local and parallel finite element method based on the partition of unity for incompressible flow[J], J. Sci. Comput., DOI: 10.1007/s10915-014-9979-x

16. Haibiao Zheng, Lina Song, Yanren Hou, Yuhong Zhang. The partition of unity  parallel finite element algorithm[J], Adv. Comp. Math., DOI 10.1007/s10444-014-9392-x

17. Feng Shi, Haibiao Zheng, Jiaping Yu, Ying Li, On the convergence of  Variational multiscale methods based on Newton's iteration  for the incompressible flows[J]. Appl. Math. Model., 2014, 38: 5726–5742.

18. Cong Xie, Haibiao Zheng, A parallel variational multiscale method for incompressible fows based on the partition of unity.  Int. J. Numer. Anal. Model., 2014, 11, 854-865.

19. Li Shan, Haibiao Zheng, Jiaping Yu. Second-order partitioned time stepping methods for a parabolic two domain problem[J], Numer. Meth.PDEs,submit to