Shun Zhang

About Me

I am a Postdoc at the Division of Applied Mathematics, Brown University, working with Professor Jan S. Hesthaven. I got my Ph.D. degree from Department of Mathematics, Purdue University in 2009 under the direction of Professor Zhiqiang Cai with a dissertation on the recovery-based a posteriori error estimators for finite element methods. Before this, I got my Bachelor and Master's degrees in mathematics from Tongji University, Shanghai, China.

At the annual meeting of the Society for Industrial and Applied Mathematics (SIAM) in Denver, Colorado, July 6-10, 2009, I won the 2009 SIAM Student Paper Prize for the paper entitled "Recovery-Based Error Estimator for Interface Problems: Conforming Linear Elements", co-authored with my advisor, Professor Zhiqiang Cai.

From June 2013, I will be an assistant professor at Department of Mathematics of City University of Hong Kong. My new e-mail address is shun.zhang AT cityu.edu.hk

Contact

Division of Applied Mathematics
Brown University, Box F
182 George Street
Providence, RI 02912

Office: 180 George St, Room 18
401 863 2250
E-mail: Shun_Zhang at Brown.edu

Curriculum Vitae

cv in pdf

Teaching

AMPA0340: METHODS OF APPLIED MATHEMATICS II

2821O: TOPICS IN A POSTERIORI ERROR ESTIMATIONS: FINITE ELEMENT & REDUCED BASIS METHOD

Research

I work on numerical solutions of partial differential equations. My current research focuses on a posteriori error estimations, adaptive methods for finite element methods, and reduced basis methods.

• Papers

  (with Jan Hesthaven ) On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations, see also Brown Division of Applied Math Scientific Computing Tech Report 2011. J. Sci. Comput., submitted
  Efficient greedy algorithms for successive constraints methods with high-dimensional parameters. Brown Division of Applied Math Scientific Computing Tech Report 2011-23.
  (with Jan Hesthaven and Benjamin Stamm ) Certified reduced basis methods for the electric field integral equation. Brown Division of Applied Math Scientific Computing Tech Report 2011-21. SIAM J. Sci. Comput., Vol. 34, No. 3, pp. A1777--A1799
  (with Jan Hesthaven and Benjamin Stamm ) Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods, Brown Division of Applied Math Scientific Computing Tech Report 2011-15. ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), submitted
  (with Zhiqiang Cai ) Quasi-robust a posteriori error estimator for the nonlinear Poisson-Boltzmann equation,
  (with Zhiqiang Cai ) A note on discontinuous Galerkin methods, submitted.
  (with Zhiqiang Cai ) Robust equilibrated residual error estimator for diffusion problems: Conforming elements, SIAM J. Numer. Anal. Vol. 50, No.1 pp. 151-170, 2012.
  (with Zhiqiang Cai ) Mixed methods for Stokes and Navier-Stokes equations based on pseudostress-pressure-velocity formulation, Math. Comp., Posted: March 28, 2012.
  (with Zhiqiang Cai and Xiu Ye) Discontinuous Galerkin finite element methods for interface problems: A priori and a posteriori error estimations, SIAM J. Numer. Anal., Vol 49, No.5, pp. 1761-1787, 2011.
  (with Zhiqiang Cai) Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps, DOI: 10.1002/num.20629, Article first published online: 25 OCT 2010, Numerical Methods for Partial Differential Equations, Volume 28, Issue 2, pages 476Ð491, March 2012
  (with Zhiqiang Cai) Flux recovery and a posteriori error estimators: Conforming elements for scalar elliptic equations, SIAM J. Numer. Anal., Vol. 48, No. 2, pp. 578--602, 2010
  (with Zhiqiang Cai and Chunbo Wang) Mixed finite element methods for incompressible flow: Stationary Navier-Stokes equations , SIAM J. Numer. Anal, Vol. 48, No. 1, pp. 79--94, 2010.
  (with Zhiqiang Cai) Recovery-based error estimators for interface problems: Mixed and nonconforming finite elements, SIAM J. Numer. Anal, Vol. 48, No. 1, pp. 30--52, 2010.
  (with Zhiqiang Cai) Recovery-based error estimators for interface problems: Conforming linear elements, SIAM J. Numer. Anal., Vol. 47, No. 3, pp. 2132--2156, 2009.
  Mortar finite element methods for Stokes problems (in Chinese), Master Thesis, Department of Mathematics, Tongji Univ., 2003.
  (With Y. Shu, Z. Huang, and W. Wu) A mortar finite element method for linear Poisson-Boltzmann equation, Comm. on Appl. Math. and Comput.16(2002), 1-8.
  (With S. Chen and Z. Huang) Deduction and computation of strongly implicit procedure method for seven-diagonal finite difference method of 3 dimensions, J. of Tongji Univ. , 29(2001), 857-861. (This is a paper based on my undergraduate thesis.)

• Presentations Slides

  Robust recovery based a posteriori error estimators for finite element methods, SIAM Student Paper Prize presentation, 2009 SIAM Annual Meeting, Denver, CO, pdf file
  Recovery-based error estimators for interface problems: Mixed and nonconforming finite elements, Finite Element Circus, RPI, 2008, pdf file
  Flux Recovery based error estimators for higher order FEMs, 2008 SIAM Annual Meeting, San Diego, pdf file