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
streamline-diffusion 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: 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
- 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 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.
#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. 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
#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 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.
#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 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: 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 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: 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 Runge-Kutta 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. 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
- personal web page
#11: Chen, Min-Hung: Ph.D.
in Mathematics completed in 2005.
- 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
- personal web page
#12: Yenikaya, Bayram:
Ph.D.
in Mathematics completed in January 2005.
- Duration of Ph. D.
work: Fall
2001-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.
#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. 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: 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
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.,
226 (2007), pp. 1027-1058.
- 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
convection-diffusion problems, J. Sci. Comput., 32 (2007), pp. 233-262.
- Optimal
convergence of the original discontinuous Galerkin method for the
transport-reaction equation on special meshes, SIAM J. Numer. Anal., 46 (2008), pp. 1250-1265.
- A superconvergent
LDG-hybridizable Galerkin method for second-order elliptic problems, Math. Comp. , 77 (2008), pp. 1887-1916.
- 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: Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains.
- Papers resulting from
the
Dissertation:
- Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains,
J. Sci. Comput., 42(2010), pp. 144-184.
- 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 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., 45(2007), pp. 1742-1776.
- The computation
of a locally conservative stress for the continuous Galerkin method for
compressible linearly elastic materials, J. Sci. Comput., 36 (2008), pp. 151-163.
- Superconvergent discontinuous Galerkin methods for second-order elliptic problems, Math. Comp. , 78 (2009), pp. 1-24.
#18: Soon,
See-Chew: 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 one-dimensional case, J. Sci. Comput., 32 (2007), pp. 201-232.
- 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 one-dimensional case, J. Sci. Comput., 32 (2007), pp. 201-232.
#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 time-dependent Hamilton-Jacobi equations.
- Papers resulting from
the
Dissertation:
-
Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations,
Math. Comp.
,
82 (2013), pp. 1287-212.
- 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. A28-A47.
- Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains, SIAM J. Sci. Comput., 34 (2012), pp. A497-A519.
- Solving convection-diffusion problems on curved domains by extensions from subdomains, J. Sci. Comput., 59 (2014) , pp. 512-543
- Current position:
Assistant Professor, University of
Concepcion, Chile.
- email address: msolano@ing-mat.udec.cl
- personal web page
#22: Shi, Ke: Ph.D.
in Mathematics completed in 2012.
- Duration of Ph. D.
work: Fall
2008-2012
- 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. 1-37.
-
A projection-based error analysis of HDG methods for Timoshenko beams,
Math. Comp.
,
81 (2012), pp. 131-151.
-
Conditions for superconvergence of HDG methods for second-order elliptic problems,
Math. Comp.
,
81 (2012), 1327-1353.
-
Superconvergent HDG methods on isoparametric elements for second-order elliptic problems,
SIAM J. Numer. Anal.
,
50 (2012), pp. 1417-1432.
-
Conditions for superconvergence of HDG methods for Stokes flow,
Math. Comp.
,
82 (2013), pp. 651-671.
-
Superconvergent HDG methods for linear elasticity with weakly symmetric stresses,
IMA J. Numer. Anal.
,
33 (2013), pp. 747-770.
- 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 second-order elliptic equations.
- Papers resulting from
the
Dissertation:
-
A posteriori error estimates for HDG methods,
J. Sci. Comput.
,
51 (2012), pp. 582-607 .
-
A posteriori error analysis for hybridizable discontinuous Galerkin methods for second order elliptic problems,
SIAM J. Numer. Anal.
,
51 (2013), pp. 676-693 .
-
An a posteriori error estimate for the variable-degree Raviart-Thomas method,
Math. Comp.
,
83 (2014), pp. 1063-1082 .
-
Contraction property of adaptive hybridizable discontinuous Galerkin methods,
Math. Comp.
,
85 (2016), pp. 1113-1141.
- 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 M-decompositions.
Papers resulting from
the
Dissertation:
-
Superconvergence by M-decompositions. Part I: General theory for HDG methods for diffusion,
Math. Comp.
,
86 (2017), pp. 1609-1641.
-
Superconvergence by M-decompositions. Part II: Construction of two-dimensional finite elements,
ESAIM Math. Model. Numer. Anal.
,
51 (2017), pp. 165-186.
-
Superconvergence by M-decompositions. Part III: Construction of three-dimensional finite elements,
ESAIM Math. Model. Numer. Anal.
,
51 (2017), pp. 365-398.
-
A note on the devising of superconvergent HDG methods for Stokes flow by M-decompositions,
IMA J. Numer. Anal.
,
37 (2017), pp. 730-749.
-
Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by M-decompositions,
IMA J. Numer. Anal.
,
38 (2018), pp. 566-604.
-
A systematic construction of finite element commuting exact sequences,
SIAM J. Numer. Anal.
,
55 (2017), pp. 1650-1688.
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. 377-393.
#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 p-Laplacian,
SIAM J. Sci. Comput.
,
38 (2016), pp. A545-A566.
-
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