My Students
List of Ph.D. Students:
The Mathematics Genealogy Project.
#1: Sun, Peter Min: Ph.
D. in Mathematics completed in 1988.
 Duration of Ph. D.
work: Fall
1986 Summer 1988.
 Dissertation's title: A
streamlinediffusion method for miscible and immiscible flow in porous
media.
#2: Hou, Suchung: Ph.D.
in Mathematics completed in 1991.
 Duration of Ph. D.
work: Fall
1988 Summer 1991.
 Dissertation's title: A
Finite Element Method for Conservation Laws: Multidimensional Case.
 Papers resulting from the
Dissertation:
 TVB RungeKutta
Local Projection
Discontinuous Galerkin Finite Element Method for Conservation Laws IV:
The Multidimensional Case, Math.
Comp., 54 (1990), pp. 545581.
 Current position: Associate Professor
of Mathematics, National Cheng Kung University,
Taiwan.
 email address: schou@mail.ncku.edu.tw
 personal web page
#3: Triandaf, Ioana: Ph.D.
in Mathematics completed in 1991.
 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 driftdiffusion semiconductor device equations,Math.
Comp., 59 (1992), pp. 383401.
 Error
estimates for a finite element method for the driftdiffusion
semiconductor
device equations: The zero diffusion case, Math.
Comp., 63 (1994), pp. 5176.
 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.
#4: Gau, Kristy Huiing:
Ph.D.
in Mathematics completed in 1995.
 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. 3747.
 A model
numerical
scheme for
the propagation of phase transitions in solids, SIAM
J. Sci. Comput.,17 (1996), pp.
10921121.
 Current position: Mathematical
Engineer,
General Electrics Aircraft
Engines.
 email address: kristy.gau@ae.ge.com
#5: Etcheverry, Javier:
Ph.D. in Mathematics completed in 2000.
 Ph.D. of the Universidad de BuenosAires
 Dissertation's title: Un nuevo método de aproximación de soluciones de Ecuaciones Parabólicas No Lineales.
 Current position: Professor of Mathematics, U. of Buenos Aires, Argentina.
 email address: jetchev@dm.uba.ar
 personal web page
#6: Yang, Xiangrong:
Ph.D. in Mathematics completed in 2000.
 Duration of Ph. D.
work: Fall
1996 Winter 2000.
 Dissertation's title: Analysis
of Numerical Methods for Nonlinear Hyperbolic Conservation Laws.
 Papers resulting from the
Dissertation:
 A priori error
estimates for
hyperbolic conservation laws. Part III: Multidimensional
fluxsplitting
monotone schemes in nonCartesian grids, SIAM
J. Numer. Anal., 35 (1998), pp.
17751803.
 Current position: Software
Developer, Computer Associates, Califormia.
#7: Albert, Samuel: Ph.D.
in Mathematics completed in 2001.
 Duration of Ph. D.
work: Fall
1998  Summer 2000.
 Dissertation's title: A
posteriori error estimates for HamiltonJacobiBellman equations.
 Papers resulting from the
Dissertation:
 A posteriori
error
estimates
for general numerical methods for HamiltonJacobi equations. Part I:
The
steadystate case, Math. Comp., 27
(2001), pp. 4976.
 A posteriori
error
estimates
for general numerical methods for HamiltonJacobi equations. Part II:
The
transient case, Finite Volumes for
Complex
Application III, Herbin and D.
Kroner,
Eds., Hermes Penton Science (2002), pp. 1724.
 Current position: Barclays.
#8: Castillo, Paul: Ph.D. in Scientific Computing completed in 2001.
 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 hpversion of the local discontinuos Galerkin method for
convectiondiffusion problems,Math.
Comp., 71
(2002), pp. 455478.
 The local
discontinuous Galerkin
method fr contaminant transport problems, Advances
in Water Resources, 24 (2000),
pp.
7387.
 An a priori
error
analysis of
the local discontinuos Galerkin method for elliptic problems,
SIAM J. Numer. Anal., 38
(2000),
pp. 16761706.
 Performance of
discontinuous
Galerkin methods for elliptic problems, SIAM
J. Sci. Comput., 24 (2002),
pp.
624547.
 Current position: Professor, University of Puerto Rico,
Mayagüez, Puerto Rico.
 email address: paul.castillo@upr.edu
 personal web page
#9: Ortigoza, Gerardo: Ph.D. in Mathematics completed in 2003.
 Duration of Ph. D.
work: Fall
1998  Spring 2001.
 Main Adviser: Fernando Reitich, School of Mathematics.
 Dissertation's title: The RungeKutta Discontinuous Galerkin Method for Maxwell Equations.
#10: Celiker, Fatih: Ph.D.
in Mathematics completed in 2005.
 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. 221231 .
 Elementbyelement
postprocessing of Discontinuous
Galerkin methods for Timoshenko beams, J. Sci. Comput., 27 (2006), pp. 177187.
 Superconvergence
of the numerical traces of Discontinuous Galerkin and hybridized
mixed methods for convectiondiffusion problems in one space dimension, Math.
Comp., 76
(2007), pp. 6796.
 Lockingfree
optimal Discontinuous Galerkin methods for Timoshenko beams, SIAM J. Numer.
Anal. ,
44 (2006), pp. 22972325.
 Current position: Associate Professor, Wayne State
University.
 email address: celiker@math.wayne.edu
 personal web page
#11: Chen, MinHung: Ph.D.
in Mathematics completed in 2005.
 Duration of Ph. D.
work: Fall
2001 Spring 2005.
 Dissertation's title: RungeKutta
discontinuous Galerkin methods for Maxwell's equations.
 Papers resulting from
the
Dissertation:
 RungeKutta
discontinuous Galerkin methods for Maxwell's equations, J. Sci. Comput, 22/23
(2005),
pp. 205226.
 Current position: Associate Professor,
National Cheng Kung University, Taiwan.
 email address: mhchen@math.ncku.edu.tw
 personal web page
#12: Yenikaya, Bayram:
Ph.D.
in Mathematics completed in January 2005.
 Duration of Ph. D.
work: Fall
2001Fall 2004.
 Dissertation's title: Adaptive
methods for HamiltonJacobi equations.
 Papers resulting from the
Dissertation:
 An adaptive
method with
rigorous error control for the HamiltonJacobi equations. Part I: The
onedimensional steady state case, Appl.
Numer. Math., 52 (2005), pp. 175195.
 An
adaptive
method with
rigorous error control for the HamiltonJacobi equations. Part II: The
twodimensional steady state case, J.
Comput. Phys., 209 (2005),
pp. 391405.
 Current position: Software Developer,
Cadence Design Systems Inc., San Jose, California.
#13: Guzey, Sukru: Ph.D.
in Civil Engineering completed in 2006.
 Duration of Ph. D.
work: Fall
2002 Spring 2005.
 Main Adviser: Henryk Stolarski, Civil Engineering.
.
 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. 221231 .
 Elementbyelement
postprocessing of Discontinuous
Galerkin methods for Timoshenko beams, J. Sci. Comput., 27 (2006), pp. 177187.
 Superconvergence
of the numerical traces of Discontinuous Galerkin and hybridized
mixed methods for convectiondiffusion problems in one space dimension, Math.
Comp., 76
(2007), pp. 6796.
 Lockingfree
optimal Discontinuous Galerkin methods for Timoshenko beams, SIAM J. Numer.
Anal. ,
44 (2006), pp. 22972325.
 Current position: Assistant Professor, Purdue
University.
 email address: guzey@purdue.edu
 personal web page
#14: Chen, Yanlai: Ph.D.
in Mathematics completed in 2007.
 Duration of Ph. D.
work: Summer
2004 Spring 2007.
 Dissertation's title: Adaptive
highorder accurate methods for HamiltonJacobi equations.
 Papers resulting from
the
Dissertation:
 An adaptive
high order discontinuous Galerkin method with error control for the
HamiltonJacobi equations, J.
Comput. Phys.,
226 (2007), pp. 10271058.
 Current position: Associate Professor, University of Massachusetts, Dartmouth.
 email address: Yanlai.Chen@umassd.edu
 personal web page
#15: Dong,
Bo: Ph.D.
in Mathematics completed in 2007.
 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
convectiondiffusion problems, J. Sci. Comput., 32 (2007), pp. 233262.
 Optimal
convergence of the original discontinuous Galerkin method for the
transportreaction equation on special meshes, SIAM J. Numer. Anal., 46 (2008), pp. 12501265.
 A superconvergent
LDGhybridizable Galerkin method for secondorder elliptic problems, Math. Comp. , 77 (2008), pp. 18871916.
 Current position: Associate Professor, University of Massachusetts, Dartmouth.
 email address: bdong@umassd.edu
 personal web page
#16: Gupta, Deepa: Ph.D.
in Mathematics completed in 2007.
 Duration of Ph. D.
work: Fall
2004 Fall 2007.
 Main Adviser: Fernando Reitich, School of Mathematics.
.
 Dissertation's title: BoundaryConforming Discontinuous Galerkin Methods via Extensions from Subdomains.
 Papers resulting from
the
Dissertation:
 BoundaryConforming Discontinuous Galerkin Methods via Extensions from Subdomains,
J. Sci. Comput., 42(2010), pp. 144184.
 Current position: Boston Scientific, Minneapolis.
#17: Wang, Haiying: Ph.D.
in Mathematics completed in 2007.
 Duration of Ph. D.
work: Fall
2003 Fall 2006.
 Dissertation's title: H(div)postprocessing
and hybridization
of the continuous Galerkin methods for secondorder elliptic and linear
elasticity problems.
 Papers resulting from
the
Dissertation:
 Locally
conservative fluxes for the continuous
Galerkin method for secondorder elliptic problems, SIAM J. Numer. Anal., 45(2007), pp. 17421776.
 The computation
of a locally conservative stress for the continuous Galerkin method for
compressible linearly elastic materials, J. Sci. Comput., 36 (2008), pp. 151163.
 Superconvergent discontinuous Galerkin methods for secondorder elliptic problems, Math. Comp. , 78 (2009), pp. 124.
#18: Soon,
SeeChew: Ph.D.
in Mathematics completed in 2008.
 Duration of Ph. D.
work: Fall
2003 Spring 2008.
 Main Adviser: Henryk Stolarski, Civil Engineering.
.
 Dissertation's title: Hybridizable Discontinuous Galerkin Method for Solid Mechanics.
 Papers resulting from
the
Dissertation:
 Adjoint
recovery of superconvergent linear functionals from Galerkin
approximations. The onedimensional case, J. Sci. Comput., 32 (2007), pp. 201232.
 Current position:
Caterpillar, Illinois.
#19: Ichikawa,
Ryuhei: Ph.D.
in Mathematics completed in 2010.
 Duration of Ph. D.
work: Fall
2003 Spring 2010 .
 Dissertation's title: Adjoint recovery of superconvergent linear
linear functionals from Galerkin approximations.
 Papers resulting from
the
Dissertation:
 Adjoint
recovery of superconvergent linear functionals from Galerkin
approximations. The onedimensional case, J. Sci. Comput., 32 (2007), pp. 201232.
#20: Merev, Ivan: Ph.D.
in Mathematics completed in 2010.
 Duration of Ph. D.
work: Summer
2007 Spring 2010
 Dissertation's title: A posteriori error estimates
for timedependent HamiltonJacobi equations.
 Papers resulting from
the
Dissertation:

Local a posteriori error estimates for timedependent HamiltonJacobi equations,
Math. Comp.
,
82 (2013), pp. 1287212.
 Current position:
Bloomberg, New York.
#21: Solano,
Manuel: Ph.D.
in Mathematics completed in 2011.
 Duration of Ph. D.
work: Fall
2008 Spring 2011 .
 Dissertation's title: HDG methods
for curved domains.
 Papers resulting from
the
Dissertation:
 Coupling at a distance HDG and BEM
, SIAM J. Sci. Comput., 34 (2012), pp. A28A47.
 Solving Dirichlet Boundaryvalue Problems on Curved Domains by Extensions from Subdomains, SIAM J. Sci. Comput., 34 (2012), pp. A497A519.
 Solving convectiondiffusion problems on curved domains by extensions from subdomains, J. Sci. Comput., 59 (2014) , pp. 512543
 Current position:
Assistant Professor, University of
Concepcion, Chile.
 email address: msolano@ingmat.udec.cl
 personal web page
#22: Shi, Ke: Ph.D.
in Mathematics completed in 2012.
 Duration of Ph. D.
work: Fall
20082012
 Dissertation's title: Devising superconvergent HDG methods for partial differential equations
 Papers resulting from
the
Dissertation:

Hybridizable discontinuous Galerkin methods for Timoshenko beams,
J. Sci. Comput.
,
44 (2010), pp. 137.

A projectionbased error analysis of HDG methods for Timoshenko beams,
Math. Comp.
,
81 (2012), pp. 131151.

Conditions for superconvergence of HDG methods for secondorder elliptic problems,
Math. Comp.
,
81 (2012), 13271353.

Superconvergent HDG methods on isoparametric elements for secondorder elliptic problems,
SIAM J. Numer. Anal.
,
50 (2012), pp. 14171432.

Conditions for superconvergence of HDG methods for Stokes flow,
Math. Comp.
,
82 (2013), pp. 651671.

Superconvergent HDG methods for linear elasticity with weakly symmetric stresses,
IMA J. Numer. Anal.
,
33 (2013), pp. 747770.
 Current position: Assistant Professor, Old Dominion University.
 email address: kshi@odu.edu
 personal web page
#23: Zhang, Wujun: Ph.D.
in Mathematics completed in 2012.
 Duration of Ph. D.
work: Fall 2008 Spring 2012
 Dissertation's title: Convergence of adaptive hybridizable discontinuous Galerkin methods for secondorder elliptic equations.
 Papers resulting from
the
Dissertation:

A posteriori error estimates for HDG methods,
J. Sci. Comput.
,
51 (2012), pp. 582607 .

A posteriori error analysis for hybridizable discontinuous Galerkin methods for second order elliptic problems,
SIAM J. Numer. Anal.
,
51 (2013), pp. 676693 .

An a posteriori error estimate for the variabledegree RaviartThomas method,
Math. Comp.
,
83 (2014), pp. 10631082 .

Contraction property of adaptive hybridizable discontinuous Galerkin methods,
Math. Comp.
,
85 (2016), pp. 11131141.
 Current position: Assistant Professor, Rutgers University.
 email address: wujun@math.rutgers.edu
 personal web page
#24: Fu,
Guosheng: Ph.D.
in Mathematics completed in 2016.
 Duration of Ph. D.
work: Fall
2013 Spring 2016 .
 Dissertation's title: Devising superconvergent HDG methods by Mdecompositions.
 Papers resulting from
the
Dissertation:

Superconvergence by Mdecompositions. Part I: General theory for HDG methods for diffusion,
Math. Comp.
,
86 (2017), pp. 16091641.

Superconvergence by Mdecompositions. Part II: Construction of twodimensional finite elements,
ESAIM Math. Model. Numer. Anal.
,
51 (2017), pp. 165186.

Superconvergence by Mdecompositions. Part III: Construction of threedimensional finite elements,
ESAIM Math. Model. Numer. Anal.
,
51 (2017), pp. 365398.

A note on the devising of superconvergent HDG methods for Stokes flow by Mdecompositions,
IMA J. Numer. Anal.
,
37 (2017), pp. 730749.

Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by Mdecompositions,
IMA J. Numer. Anal.
,
38 (2018), pp. 566604.

A systematic construction of finite element commuting exact sequences,
SIAM J. Numer. Anal.
,
55 (2017), pp. 16501688.
 Current Position:
Postdoc. , Brown University.
 email address: Guosheng_Fu@Brown.edu
 personal web page
#25: Nour,
Maher: Ph.D.
in Mathematics completed in 2016.
 Main adviser: Kassem Mustapha, KFUPM.
 Dissertation's title: Discontinuous Galerkin Method for Fractional Diffusion Probem.
 Papers resulting from
the
Dissertation:

Convergence and superconvergence analyses of HDG methods for time
fractional diffusion problems,
Adv. Comput. Math.
,
42 (2016), pp. 377393.
#26: Shen,
Jiguang: Ph.D.
in Mathematics completed in 2017.
 Duration of Ph. D.
work: Fall
2014 Spring 2017 .
 Dissertation's title: HDG methods
for nonlinear elasticity.
 Papers resulting from
the
Dissertation:

A hybridizable discontinuous Galerkin method for the pLaplacian,
SIAM J. Sci. Comput.
,
38 (2016), pp. A545A566.

An algorithm for stabilizing hybridizable discontinuous Galerkin method for nonlinear Elastiticty,
Submitted.
 Current position:
Microsoft, Seattle.
#27: Xia,
Shiqiang: Ph.D.
in Mathematics to completed in the near future.
 Duration of Ph. D.
work: Fall
2017 ... .
 Dissertation's title:
 Papers resulting from
the
Dissertation:
 Current position:
Graduate Student, University of
Minnesota.
 email address: xiaxx268@umn.edu
 personal web page