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 2009: Math351-011 ENGINEERING MATHEMATICS I .
  • Spring 2009: Math353-012 ENGINEERING MATHEMATICS III .

• My Research
  • Published recently:
    • Zhang, Shangyou A family of $Q_{k+1,k}\times Q_{k,k+1}$ divergence-free finite elements on rectangular grids. SIAM J. Num. Anal., 47 (2009), 2090-2107. pdf
    • Zhang, Shangyou A family of 3D continuously differentiable finite elements on tetrahedral grids. Appl. Numer. Math. 59 (2009), no. 1, 219--233.
    • Gilbert, Robert P.; Wirgin, Armand; Xu, Yongzhi; Zhang, Shangyou A mathematical model for evaluation of osteoporosis. Discrete and computational mathematics, 1--16, Nova Sci. Publ., New York, 2008.
    • Zhang, Shangyou On the P1 Powell-Sabin divergence-free finite element for the Stokes equations. J. Comput. Math. 26 (2008), no. 3, 456--470.
    • Olagunju, David O.; Vyas, Anand B.; Zhang, Shangyou Analytical and numerical solutions for torsional flow between coaxial discs with heat transfer. SIAM J. Appl. Math. 68 (2008), no. 5, 1404--1422.
    • Zhang, Shangyou A $C1$-$P2$ finite element without nodal basis. M2AN Math. Model. Numer. Anal. 42 (2008), no. 2, 175--192.
    • Qin, Jinshui; Zhang, Shangyou On the selective local stabilization of the mixed Q1-P0 element. Internat. J. Numer. Methods Fluids 55 (2007), no. 12, 1121--1141.
    • Zhang, Shangyou Numerical integration with Taylor truncations for the quadrilateral and hexahedral finite elements. J. Comput. Appl. Math. 205 (2007), no. 1, 325--342.
    • Qin, Jinshui; Zhang, Shangyou Stability and approximability of the $\scr P\sb 1$-$\scr P\sb 0$ element for Stokes equations. Internat. J. Numer. Methods Fluids 54 (2007), no. 5, 497--515.
    • Gilbert, Robert P.; Xu, Yongzhi; Zhang, Shangyou Computing porosity of cancellous bone using ultrasonic waves. J. Appl. Funct. Anal. 2 (2007), no. 2, 185--195.
    • Duan, Huo-Yuan; Gao, Shao-Qin; Tan, Roger C. E.; Zhang, Shangyou A generalized BPX multigrid framework covering nonnested V-cycle methods. Math. Comp. 76 (2007), no. 257, 137--152.
  • 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)
  • On the full $C_1$-$Q_k$ finite element spaces on rectangles and boxes.(2/2007)
  • Divergence-free finite elements on tetrahedral grids for $k\ge 6$ (6/2008,6/2009)
  • Bases for C0-P1 divergence-free elements and for C1-P2 finite elements on union jack grids (6/2008,6/2009)
  • Quadratic divergence-free finite elements on Powell-Sabin tetrahedral grids (10/2008,6/2009)
  • (with C. Bacuta, P.S. Vassilevski) A New Approach for Solving Stokes Systems Arising From a Distributive Relaxation Method (12/2008)
  • (with Xuejun Xu) Computing Darcy-Stokes flow by divergence-free finite elements (1/2009,7/2009)
  • A family of continuously differentiable finite elements on simplicial grids in four space dimensions (7/2009)
  • On the jump-independence of the weighted $L^2$ projection (10/2009)
  • A lowest order divergence-free finite element on rectangular grids (10/2009)

• Other services:
  • International Society for Analysis, its Application & Computation
  • University of Delaware Asian and Pacfic Islanders Caucus
  • North American Chinese Soccer League.
  • Delaware Chinese Festival.
  • University of Science and Technology of China Alumni Foundation.
  • USTC class 771.
  • Philadelphia Chinese Computer Professionals.

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