Shun Zhang

About Me

I am a PostDoc at the Department of Mathematics, Purdue University, working with my thesis advisor Prof. Zhiqiang Cai in the area of Finite Element Methods. I got my Ph.D. degree from Department of Mathematics, Purdue University, 2009. 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, I win 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.

Contact

Department of Mathematics
Purdue University
150 North University Street
West Lafayette, IN 47907-2067

Office: Math 413
Email: zhang at math.purdue.edu

Curriculum Vitae

Pdf file

Research

Research Statement


I work on numerical solutions of partial differential equations. My current research focuses on A Posteriori error estimations and adaptive methods for finite element methods.

• Papers

  (with Zhiqiang Cai ) Quasi-robust a posteriori error estimator for the nonlinear Poisson-Boltzmann equation,
  (with Zhiqiang Cai and Xiu Ye) Discontinuous Galerkin finite element methods for interface problems: A priori and a posteriori error estimations,
  (with Zhiqiang Cai) Robust residual- and recovery-based a posteriori error estimators for interface problems with flux jumps, Numer. Methods PDE, submitted.
  (with Zhiqiang Cai) Flux recovery and a posteriori error estimators: conforming elements for scalar elliptic equations, SIAM J. Numer. Anal., submitted.
  (with Zhiqiang Cai) Recovery-based error estimators for interface problems: Mixed and nonconforming finite elements, pdf, SIAM J. Numer. Anal., submitted.
  (with Zhiqiang Cai) Recovery-based error estimators for interface problems: Conforming linear elements, pdf, SIAM J. Numer. Anal., Vol. 47, No. 3, pp. 2132-2156, 2009.
  (with Zhiqiang Cai and Chunbo Wang) Mixed finite element methods for incompressible flow: Stationary Navier-Stokes equations, submitted.
  (with Zhiqiang Cai ) Mixed methods for Stokes and Navier-Stokes equations based on pseudostress-pressure-velocity formulation
  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