My Students

• Duration of Ph. D. work:  Fall 1986- Summer 1988.
• Dissertation's title: A streamline-diffusion method for miscible and immiscible flow in porous media.

• Duration of Ph. D. work:  Fall 1988- Summer 1991.
• Dissertation's title: A Finite Element Method for Conservation Laws: Multi-dimensional Case.

• Papers resulting from the Dissertation:
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws IV: The Multidimensional Case, Math. Comp., 54 (1990), pp. 545-581.
• Current position: Associate Professor of Mathematics, National Cheng Kung University, Taiwan.
• email address: schou@mail.ncku.edu.tw

• Duration of Ph. D. work:  Fall 1988- Summer 1991.
• Dissertation's title: A Finite Element Method for Numerically Solving the Semiconductor Device Equations.
• Papers resulting from the Dissertation:
• Convergence of a finite element method for the drift-diffusion semiconductor device equations,Math. Comp., 59  (1992), pp. 383-401.
•  Error estimates for a finite element method for the drift-diffusion semiconductor device equations: The zero diffusion case, Math. Comp., 63 (1994), pp. 51-76.
• Current position: Researcher, Navy Research Laboratory.  
• email address: triandaf@nls4.nrl.navy.mil
• Awards: Recipient of the 2004 Invention Award  and of the 2005 Alan Berman Research Publication Award. Both awards are granted by NRL.

• Duration of Ph. D. work:  Fall 1992- Summer 1995.
• Dissertation's title: Numerical Methods for Conservation Laws of Mixed Type.
• Papers resulting from the Dissertation:
• A  posteriori error estimates for general numerical methods for scalar conservation laws, Mat. Aplic. Comp.,14 (1995), pp. 37-47.
• A model numerical scheme for the propagation of phase transitions in solids, SIAM J. Sci. Comput.,17 (1996), pp. 1092-1121.
• Current position: Mathematical Engineer, General Electrics Aircraft Engines.
• email address: kristy.gau@ae.ge.com

• Duration of Ph. D. work:  Fall 1996- Winter 2000.
• Dissertation's title: Analysis of Numerical Methods for Non-linear Hyperbolic Conservation Laws.
• Papers resulting from the Dissertation:
• A priori error estimates for hyperbolic conservation laws. Part III: Multidimensional flux-splitting  monotone schemes in non-Cartesian grids, SIAM J. Numer. Anal., 35 (1998), pp. 1775-1803.
• Current position: Software Developer, Computer Associates, Califormia.
  
• email address: [to be updated]

• Duration of Ph. D. work:  Fall 1998 - Summer 2000.
• Dissertation's title: A posteriori error estimates for Hamilton-Jacobi-Bellman equations.
• Papers resulting from the Dissertation:
• A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady-state case, Math. Comp., 27 (2001),  pp. 49-76.
• A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part II: The transient case, Finite Volumes for Complex Application III, Herbin and D. Kroner, Eds.,  Hermes Penton Science (2002), pp. 17--24.
• Current position: [to be updated]
  
• email address:  [to be updated]

• Duration of Ph. D. work:  Fall 1998 - Spring 2001.
• Dissertation's title: The local discontinuous Galerkin method for elliptic problems.
• Papers resulting from the Dissertation:
• Optimal a priori error estimates for the hp-version of the  local discontinuos Galerkin method for convection-diffusion problems,Math. Comp., 71 (2002), pp. 455-478.
• The local discontinuous Galerkin method fr contaminant transport problems, Advances in Water Resources, 24 (2000),  pp. 73-87.
• An a priori error analysis of the  local discontinuos Galerkin method for elliptic problems, SIAM J. Numer. Anal., 38 (2000),  pp.  1676-1706.
• Performance of discontinuous Galerkin methods for elliptic problems,  SIAM J.  Sci. Comput., 24 (2002), pp.  624-547.
• Current position: Assistant Professor,  University of Puerto Rico, Mayagüez, Puerto Rico.
• email address: castillo@math.uprm.edu

• Duration of Ph. D. work:  Fall 2001-( end of ) Fall 2004.
  
• Dissertation's title: Adaptive methods for Hamilton-Jacobi equations.
• Papers resulting from the Dissertation:
• An adaptive method with rigorous error control for the Hamilton-Jacobi equations. Part I: The one-dimensional steady state case, Appl. Numer. Math., 52 (2005), pp. 175-195.
• An adaptive method with rigorous error control for the Hamilton-Jacobi equations. Part II: The two-dimensional steady state case, J. Comput. Phys.,  209 (2005),  pp.  391-405.
• Current position: Software Developer, Cadence Design Systems Inc., San Jose, California.
• email address: bayram.yenikaya@invarium.com

• Duration of Ph. D. work:  Fall 2001- Spring 2005.
• Dissertation's title: Runge-Kutta discontinuous Galerkin methods for Maxwell's equations.
• Papers resulting from the Dissertation:
• Runge-Kutta discontinuous Galerkin methods for Maxwell's equations, J. Sci. Comput, 22/23 (2005),  pp.  205-226.
• Current position: Associate Professor,  National Cheng Kung University, Taiwan.
  
• email address: mhchen@math.ncku.edu.tw
  

• Duration of Ph. D. work:  Fall 2002- Spring 2005.
• Dissertation's title: Discontinuous Galerkin methods for Structural Mechanics.
• Papers resulting from the Dissertation:
  
• Discontinuous Galerkin methods for Timoshenko beams, Numerical Mathematics  and Advanced Applications, ENUMATH 2003, pp. 221-231 .
• Element-by-element post-processing of Discontinuous Galerkin methods for Timoshenko beams, J. Sci. Comput., 27 (2006), pp. 177-187.
  
• Superconvergence of the numerical traces of Discontinuous Galerkin and hybridized mixed methods for convection-diffusion problems in one space dimension,  Math. Comp., 76 (2007), pp. 67-96.
• Locking-free optimal  Discontinuous Galerkin methods for Timoshenko beams, SIAM J.  Numer. Anal. ,  44 (2006), pp. 2297-2325.
  
• Current position: Associate Professor, Wayne State University.
• email address: celiker@math.wayne.edu

• Duration of Ph. D. work:  Fall 2003- Fall 2006.
• Dissertation's title: H(div)-postprocessing and hybridization of the continuous Galerkin methods for second-order elliptic and linear elasticity problems.
• Papers resulting from the Dissertation:
  • Locally conservative fluxes for the  continuous Galerkin method,  for second-order elliptic problems, SIAM J. Numer. Anal., 46 (2007), pp. 1742-1776.
  • The computation of a locally conservative stress for the continuous Galerkin method for linear elasticity , submitted.
• Current position: Postdoc, R.E.R.I. Palo Alto, California.
• email address: hywang@rerinst.org

• Duration of Ph. D. work:  Summer 2003- Spring 2007.
  
• Dissertation's title: Adaptive high-order accurate methods for Hamilton-Jacobi equations.
• Papers resulting from the Dissertation:
  • An adaptive high order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations, J. Comput. Phys.,  to appear.
• Current position: Postdoc, Brown University.
• email address: ylchen@math.umn.edu

• Duration of Ph. D. work:  Fall 2004- Spring 2007. 
• Dissertation's title: Superconvergent discontinuous Galerkin methods for elliptic problems.
  
• Papers resulting from the Dissertation:
  • An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems,  J. Sci. Comput.,  to appear.
  • Optimal convergence of the original discontinuous Galerkin method for the transport-reaction equation on special meshes, SIAM J. Numer. Anal.,  in revision.
  • A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems, Math. Comp. ,  in revision.
• Current position: Postdoc, Brown University.
• email address: bdong@math.umn.edu

• Duration of Ph. D. work:  Fall 2003- ... .
• Dissertation's title: Approximation of linear functionals by finite element methods.
• Papers resulting from the Dissertation:
  • Adjoint recovery of superconvergent linear functionals from Galerkin approximations. The one-dimensional case,  J.  Sci. Comput., to appear.
• Current position: Graduate Student, University of Minnesota.
• email address: ichikawa@math.umn.edu

• Duration of Ph. D. work:  Fall 2009- ... .
• Dissertation's title:
  
• Papers resulting from the Dissertation:
• Current position: Graduate Student, University of Minnesota.
• email address: [to be determined soon]