Shangyou Zhang Department of Mathematical   Sciences University   of   Delaware Newark ,   Delaware   19716- 2553 ,   USA Office:   Ewing 310 Phone:   (302) 831-0625 Fax:     (302) 831-4511 Email:   szhang@udel.edu

• Teaching
  • Spring 2012: Math351-013 ENGINEERING MATHEMATICS I (Linear Algebra and ODE)

• My Research
  • Published recently:
    • Article: Chuanmiao Chen; Hongling Hu; Ziqing Xie; Zhang, Shangyou A jumping multigrid method via finite element extrapolation, Int. J. Numer. Anal. Model. Series B, 2 (2011), no. 4, 281--297.
    • Article : Zhang, Shangyou Quadratic divergence-free finite elements on Powell-Sabin tetrahedral grids. Calcolo 48 (2011), no. 3, 211-244, 65N30.
    • Article: Hu, Jun; Huang, Yunqing; Zhang, Shangyou The lowest order differentiable finite element on rectangular grids. SIAM J. Numer. Anal. 49 (2011), no. 4, 1350-1368, 65N30.
    • Article : Bacuta, Constantin; Vassilevski, Panayot S.; Zhang, Shangyou A new approach for solving Stokes systems arising from a distributive relaxation method. Numer. Methods Partial Differential Equations 27 (2011), no. 4, 898-914, 65N22 (35Q35 49M27 65N06 65N55)
    • Article : Huang, Yunqing; Zhang, Shangyou A lowest order divergence-free finite element on rectangular grids. Front. Math. China 6 (2011), no. 2, 253-270. 65N30 (65N12 76D07 76M10)
    • Article: Zhang, Shangyou Divergence-free finite elements on tetrahedral grids for k ge 6. Math. Comp. 80 (2011), no. 274, 669-695. 65N30 (65N12 76M10)
    • Article : Zhang, Shangyou On the full C1-Qk finite element spaces on rectangles and cuboids. Adv. Appl. Math. Mech. 2 (2010), no. 6, 701--721. 65N30
    • Article: Xu, Xuejun; Zhang, Shangyou A new divergence-free interpolation operator with applications to the Darcy-Stokes-Brinkman equations. SIAM J. Sci. Comput. 32 (2010), no. 2, 855-874, 76M10 (65D05 65N30 76D07 76S05)
    • Article: Zhang, Shangyou A family of Qk+1,k×Qk,k+1 divergence-free finite elements on rectangular grids. SIAM J. Numer. Anal. 47 (2009), no. 3, 2090-2107. 65N30 (76D07 76M10)
    • Article: Zhang, Shangyou A family of 3D continuously differentiable finite elements on tetrahedral grids. Appl. Numer. Math. 59 (2009), no. 1, 219-233. 65N30 (65N15)
  • Unpublished:
    • Invertible Jacobian for hexahedral finite elements. Part 1. Bijectivity(5/2005)
    • Invertible Jacobian for hexahedral finite elements. Part 2. global positivity(5/2005)
    • Subtetrahedral test for the positive Jacobian of hexahedral elements (11/2005)
    • On a nested refinement of anisotropic tetrahedral grids under Hessian metrics (12/2006)
    • Bases for C0-P1 divergence-free elements and for C1-P2 finite elements on union jack grids (6/2008,6/2009)
    • A family of continuously differentiable finite elements on simplicial grids in four space dimensions (7/2009)
    • A divergence-free finite element method for a type of 3D Maxwell equations (2/2010)
    • (with Yunqing Huang, Xiangtan University) Superconvergence of the $Q_{k+1,k}$-$Q_{k,k+1}$ divergence-free finite element (9/2011)
    • (with Lizhen Qin and Zhimin Zhang, Wayne State University) Finite element methods with coordinate charts for solving elliptic equations on manifolds (9/2011)
    • (with Houde Han and Zhongyi Huang, Tsinghua University) An Iterative Method based on equation decomposition for the fourth-order singular perturbation problem. (10/2011)
    • (with Wenbin Chen, Fudan University and Xuejun Xu, Chinese Academy of Science) On a Robin-Robin domain decomposition method with optimal convergence rate (12/2011)
    • Jump-independent approximation in conforming and nonconforming finite element spaces (12/2011)
    • (with Zhimin Zhang and Qingsong Zou) Flux-conserving finite element methods (1/2012)

• Other services:
  • International Society for Analysis, its Application & Computation
  • Delaware Chinese Festival.
  • University of Science and Technology of China Alumni Foundation.
  • USTC class 771. .

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