Publications of Todd Arbogast
Department of Mathematics
and Center for Subsurface Modeling
Institute for Computational Engineering and Sciences
The University of Texas at Austin
Austin, Texas
Preprints of Recent Work

T. Arbogast, M. A. Hesse, and A. L. Taicher. Mixed methods for twophase DarcyStokes mixtures of
partially melted materials with regions of zero porosity, submitted.

T. Arbogast and A. L. Taicher. A cellcentered finite difference method for a degenerate elliptic
equation arising from twophase mixtures, submitted.
Publications in Journals and Other Refereed Works

Ch.S. Huang and T. Arbogast. An EulerianLagrangian WENO scheme for
nonlinear conservation laws, Numer. Meth. Partial Diff. Eqns., to appear. DOI 10.1002/num.22091
 Reprint: T. Arbogast and M. R. Correa. Two families
of H(div) mixed finite elements on quadrilaterals of minimal dimension, SIAM
J. Numer. Anal. 54:6 (2016), pp. 33323356. DOI 10.1137/15M1013705.
 Reprint: T. Arbogast and A. L. Taicher. A linear
degenerate elliptic equation arising from twophase mixtures, SIAM J. Numer. Anal. 54:5
(2016), pp. 31053122. DOI 10.1137/16M1067846.
 Ch.S. Huang, T. Arbogast, and Ch.H. Hung. A semiLagrangian
finite difference WENO scheme for scalar nonlinear conservation laws, J. Comput. Phys. 322
(2016), pp. 559585. DOI 10.1016/j.jcp.2016.06.027.
 T. Arbogast, D. Estep, B. Sheehan, S. Tavener. A posteriori error
estimates for mixed finite element and finite volume methods for parabolic problems coupled through
a boundary, SIAM/ASA J. Uncertainty Quantification 3 (2015), pp. 169198.
 T. Arbogast and Hailong Xiao. Twolevel mortar domain
decomposition preconditioners for heterogeneous elliptic problems, Comput. Methods
Appl. Mech. Engrg., 292 (2015), pp. 221242.
 Ch.S. Huang, F. Xiao, and T. Arbogast,
Fifth order multimoment WENO schemes for hyperbolic conservation laws,
J. Sci. Comput. 64:2 (2015), pp. 477507.
 Ch.S. Huang, T. Arbogast,
Ch.H. Hung, A reaveraged WENO reconstruction and a third order CWENO scheme
for hyperbolic conservation laws, J. Comput. Phys. 262 (2014),
pp. 291312.
 T. Arbogast, D. Estep, B. Sheehan, and S. Tavener. Aposteriori error
estimates for mixed finite element and finite volume methods for problems coupled through a boundary
with nonmatching grids, IMA J. Numer. Anal. 34 (2014), pp. 16251653.

T. Arbogast and M. Juntunen and J. Pool and M. F. Wheeler, A
discontinuous Galerkin method for twophase flow in a porous medium
enforcing H(div) velocity and continuous capillary pressure,
Comput. Geosci. 17:6 (2013), pp. 10551078.
 Reprint: T. Arbogast and
Hailong Xiao, A multiscale mortar mixed space based on homogenization
for heterogeneous elliptic problems, SIAM J. Numer. Anal., 51:1
(2013), pp. 377399.
 Reprint:
T. Arbogast, Zhen Tao, and Hailong Xiao, Multiscale mortar mixed
methods for heterogeneous elliptic problems, in Recent Advances in
Scientific Computing and Applications, H. Yang, J. Li and
E. Machorro, eds., vol. 586 of Contemporary Mathematics,
Amer. Math. Soc., Providence, Rhode Island, 2013, pp. 921.
 Reprint: T. Arbogast, Ch.S. Huang,
and Ch.H. Hung, A fully conservative EulerianLagrangian streamtube
method for advectiondiffusion problems, SIAM
J. Sci. Comput., 34:4 (2012), pp. B447B478
 Reprint: T. Arbogast,
Ch.S. Huang, and T. F. Russell, A locally conservative EulerianLagrangian
method for a model twophase flow problem in a onedimensional porous
medium, SIAM J. Sci. Comput., 34:4 (2012), pp. A1950A1974.
 Ch.S. Huang, T. Arbogast, and Jianxian
Qiu, An EulerianLagrangian WENO finite volume scheme for advection
problems, J. Comp. Phys, 231:11 (2012), pp. 40284052. DOI
10.1016/j.jcp.2012.01.030
 Reprint: T. Arbogast and
Wenhao Wang, Stability, Monotonicity, Maximum and Minimum
Principles, and Implementation of the Volume Corrected
Characteristic Method, SIAM J. Sci. Comput. 33:4 (2011),
pp. 15491573.
 T. Arbogast, Mixed
Multiscale Methods for Heterogeneous Elliptic Problems, chapter in
Numerical Analysis of Multiscale Problems, I. G. Graham, Th. Y. Hou,
O. Lakkis, and R. Scheichl, eds., Lecture Notes in Computational
Science and Engineering 83, Springer, 2011.
ISBN 9783642220609.
 Reprint: T. Arbogast,
HomogenizationBased Mixed Multiscale Finite Elements for Problems
with Anisotropy, Multiscale Modeling and Simulation 9:2 (2011),
pp. 624653.
 Reprint: T. Arbogast and
Wenhao Wang, Convergence of a fully conservative volume corrected
characteristic method for transport problems, SIAM
J. Numer. Anal., 48 (2010), pp. 797823.
 T. Arbogast
and Ch.S. Huang, A fully conservative EulerianLagrangian method for
a convectiondiffusion problem in a solenoidal field,
J. Comput. Phys. 229 (2010), pp. 34153427.
 Jichun Li, T. Arbogast, and Yunqing
Huang, Mixed methods using standard conforming finite elements,
Comp. Meth. in Appl. Mech. and Engng. 198(2009), pp. 680692.
 T. Arbogast and
M. S. M. Gomez, A discretization and multigrid solver for a
DarcyStokes system of three dimensional vuggy porous media,
Computational Geosciences 13 (2009), pp. 331348.
DOI 10.1007/s105960089121y
 R. NaimiTajdar, C. Han,
K. Sepehrnoori, T. J. Arbogast, and M. A. Miller, A Fully Implicit,
Compositional, Parallel Simulator for IOR Processes in Fractured
Reservoirs, SPE Journal 12:3 (September 2007).
 Reprint: T. Arbogast,
G. Pencheva, M. F. Wheeler, and I. Yotov, A multiscale mortar mixed
finite element method, Multiscale Modeling and Simulation 6
(2007), pp. 319346.
 T. Arbogast and
D. S. Brunson, A computatonal method for approximating a DarcyStokes
system governing a vuggy porous medium, Computational
Geosciences, 11(3) (2007), pp. 207218.
 Reprint: T. Arbogast, Ch.S. Huang,
and S.M. Yang, Improved accuracy for alternatingdirection methods
for parabolic equations based on regular and mixed finite elements,
Mathematical Models & Methods in Applied Sciences 17 (2007),
pp. 12791305
 T. Arbogast and ChiehSen
Huang, A fully mass and volume conserving implementation of a
characteristic method for transport problems, SIAM
J. Sci. Comput. 28 (2006), pp. 20012022.
 T. Arbogast and H. L. Lehr,
Homogenization of a DarcyStokes system modeling vuggy porous media,
Computational Geosciences, 10 (2006), pp. 291302.
 Reprint: T. Arbogast and
K. J. Boyd, Subgrid Upscaling and Mixed Multiscale Finite Elements,
SIAM J. Numer. Anal., 44 (2006), pp. 11501171.
 Reprint:
T. Arbogast and M. F. Wheeler, A family of rectangular mixed elements with
a continuous flux for second order elliptic problems, SIAM J. Numer. Anal.,
42 (2005), pp. 19141931.
 Reprint: T. Arbogast, Analysis of a
twoscale, locally conservative subgrid upscaling for elliptic
problems, SIAM J. Numer. Anal., 42 (2004), pp. 576598.
 T. Arbogast, An overview of
subgrid upscaling for elliptic problems in mixed form, in Current
Trends in Scientific Computing, Z. Chen, R. Glowinski, and K. Li,
eds., Contemporary Mathematics, AMS, 2003, pp. 2132.
 T. Arbogast and
S. L. Bryant, A TwoScale Numerical Subgrid Technique for Waterflood
Simulations, SPE J., Dec. 2002, pp. 446457.
 T. Arbogast, Implementation of a
Locally Conservative Numerical Subgrid Upscaling Scheme for TwoPhase
Darcy Flow, Computational Geosciences, 6 (2002), pp. 45348
 T. Arbogast, Numerical subgrid
upscaling of twophase flow in porous media, in Numerical treatment of
multiphase flows in porous media, Z. Chen et al., eds., Lecture Notes
in Physics 552, Springer, Berlin, 2000, pp. 3549.
 T. Arbogast, L. C. Cowsar, M. F. Wheeler,
and I. Yotov, Mixed finite element methods on nonmatching multiblock
grids, SIAM J. Numer. Anal., 37 (2000), pp. 12951315.
 T. Arbogast, C. N. Dawson, P. T. Keenan,
M. F. Wheeler, and I. Yotov, Enhanced cellcentered finite differences
for elliptic equations on general geometry, SIAM J. Sci. Comput.,
19 (1998), pp. 404425.
 T. Arbogast and I. Yotov, A
nonmortar mixed finite element method for elliptic problems on
nonmatching multiblock grids, Comp. Meth. in Appl. Mech. and Engng.,
149 (1997), pp. 225265.
 T. Arbogast, Computational aspects of
dualporosity models, in Homogenization and Porous Media, U. Hornung,
ed., Interdisciplinary Applied Math. Series, Springer, New York, 1997,
pp. 203223.
 T. Arbogast, M. F. Wheeler, and I. Yotov,
Mixed finite elements for elliptic problems with tensor coefficients
as cellcentered finite differences, SIAM J. Numer. Anal., 34
(1997), pp. 828852.
 T. Arbogast, S. Bryant, C. Dawson,
F. Saaf, Chong Wang, and M. Wheeler, Computational methods for
multiphase flow and reactive transport problems arising in subsurface
contaminant remediation, J. Computational Appl. Math., 74
(1996), pp. 1932,.
 T. Arbogast, M. F. Wheeler, and NaiYing
Zhang, A nonlinear mixed finite element method for a degenerate
parabolic equation arising in flow in porous media, SIAM
J. Numer. Anal., 33 (1996), pp. 16691687.
 T. Arbogast, C. N. Dawson, and
M. F. Wheeler, A parallel algorithm for two phase multicomponent
contaminant transport, Applications of Math., 40 (1995),
pp. 163174,.
 T. Arbogast and Zhangxin Chen,
On the implementation of mixed methods as nonconforming methods for
second order elliptic problems, Math. Comp., 64 (1995),
pp. 943972.
 T. Arbogast and
M. F. Wheeler, A characteristicsmixed finite element method for
advection dominated transport problems, SIAM J. Numer. Anal.,
32 (1995), pp. 404424.
 T. Arbogast, Gravitational
forces in dualporosity systems. II. Computational validation of the
homogenized model, Transport in Porous Media, 13 (1993),
pp. 205220.
 T. Arbogast, Gravitational
forces in dualporosity systems. I. Model derivation by
homogenization, Transport in Porous Media, 13 (1993),
pp. 179203.
 T. Arbogast, M. Obeyesekere, and
M. F. Wheeler, Numerical methods for the simulation of flow in
rootsoil systems, SIAM J. Numer. Anal., 30 (1993),
pp. 16771702.
 J. Douglas, Jr., T. Arbogast,
P. J. Paes Leme, J. L. Hensley, and N. P. Nunes, Immiscible
displacement in vertically fractured reservoirs, Transport in Porous
Media, 12 (1993), pp. 73106.
 T. Arbogast, The existence of
weak solutions to singleporosity and simple dualporosity models of
twophase incompressible flow, J. Nonlinear Analysis: Theory, Methods,
and Applications, 19 (1992), pp. 10091031.
 J. Douglas, Jr., J. L. Hensley, and
T. Arbogast, A dualporosity model for waterflooding in naturally
fractured reservoirs, Comp. Meth. in Appl. Mech. and Engng., 87
(1991), pp. 157174.
 J. Douglas, Jr., and
T. Arbogast, Dualporosity models for flow in naturally fractured
reservoirs, in Dynamics of Fluids in Hierarchical Porous Media,
J. H. Cushman, ed., Academic Press, London, 1990, pp. 177221.
 T. Arbogast, J. Douglas, Jr., and
U. Hornung, Derivation of the double porosity model of single phase
flow via homogenization theory, SIAM J. Math. Anal., 21 (1990),
pp. 823836.
 T. Arbogast and F. A. Milner,
A finite difference method for a twosex model of population dynamics,
SIAM J. Numer. Anal., 26 (1989), pp. 14741486.
 T. Arbogast, On the simulation
of incompressible, miscible displacement in a naturally fractured
petroleum reservoir,
R.A.I.R.O. Modél. Math. Anal. Numér, 23 (1989),
pp. 551.
 T. Arbogast, Analysis of the
simulation of single phase flow through a naturally fractured
reservoir, SIAM J. Numer. Anal., 26 (1989), pp. 1229.
Publications in Unrefereed Works
 R. NaimiTajdar, Choongyong Han,
K. Sepehrnoori, T. J. Arbogast, and M. A. Miller, A Fully Implicit,
Compositional, Parallel Simulator for IOR Processes in Fractured
Reservoirs, SPE 100079, Proceedings of the 2006 SPE/DOE Symposium on
Improved Oil Recovery, Tulsa, Oklahoma, April 2226, 2006.
 T. Arbogast and K. J. Boyd,
Mixed variational multiscale methods and multiscale finite elements,
Oberwolfach Reports, Vol. 2, Issue 1, Mathematisches
Forschungsinstitut Oberwolfach (MFO), European Mathematical Society,
Workshop on Gemischte und nichtstandard FiniteElementeMethoden mit
Anwendungen organized by K. Hackl, C. Carstensen, and D. Braess,
Extended abstract, 2005.
 Liying Zhang, S. L. Bryant,
J. W. Jennings, T. J. Arbogast, and R. Paruchuri, Multiscale flow and
transport in highly heterogeneous carbonates, SPE 90336, Proceedings
of the 2004 SPE Annual Technical Conference and Exhibition, Houston,
Texas, September 2629, 2004.
 T. Arbogast, D. S. Brunson,
S. L. Bryant, and J. W. Jennings, Jr., A preliminary computational
investigation of a macromodel for vuggy porous media, in Proceedings
of the conference Computational Methods in Water Resources XV,
C. T. Miller, et al., eds., Elsevier, 2004.
 T. Arbogast and S. L. Bryant,
Numerical subgrid upscaling for waterflood simulations, SPE 66375, in
Proceedings of the 16th SPE Symposium on Reservoir Simulation held in
Houston, Texas, Society of Petroleum Engineers, Richardson, Texas,
February 1114, 2001.
 T. Arbogast and S. Bryant,
Efficient forward modeling for DNAPL site evaluation and remediation,
in Computational Methods in Water Resources XIII, Bentley et al.,
eds., Balkema, Rotterdam, pp. 161166, 2000.
 M. Wheeler, T. Arbogast,
S. Bryant, J. Eaton, Qin Lu, M. Peszynska, and I. Yotov, A parallel
multiblock/multidomain approach for reservoir simulation, SPE 51884,
in Proceedings of the 15th SPE Symposium on Reservoir Simulation held
in Houston, Texas, Society of Petroleum Engineers, Richardson, Texas,
February 1417, 1999.
 M. F. Wheeler, T. Arbogast, S. Bryant,
and J. Eaton, Efficient parallel computation of spatially
heterogeneous geochemical reactive transport, in Computational Methods
in Water Resources XII, Vol. 1: Computational Methods in Contamination
and Remediation of Water Resources, V. N. Burganos et al., eds.,
Computational Mechanics Publications, Southampton, U.K., 1998,
pp. 453460.
 T. Arbogast, S. E. Minkoff, and
P. T. Keenan, An operatorbased approach to upscaling the pressure
equation, in Computational Methods in Water Resources XII, Vol. 1:
Computational Methods in Contamination and Remediation of Water
Resources, V. N. Burganos et al., eds., Computational Mechanics
Publications, Southampton, U.K., 1998, pp. 405412.
 Peng Wang, I. Yotov, M. Wheeler,
T. Arbogast, C. Dawson, M. Parashar, and K. Sepehrnoori, A new
generation EOS compositional reservoir simulator: Part I  Formulation
and discretization, SPE 37979, in Proceedings of the 14th SPE
Symposium on Reservoir Simulation held in Dallas, Texas, Society of
Petroleum Engineers, Richardson, Texas, June 811, 1997.
 T. Arbogast, C. N. Dawson,
P. T. Keenan, M. F. Wheeler, and I. Yotov, The application of mixed
methods to subsurface simulation, in Modeling and Computation in
Environmental Sciences, R. Helmig et al., eds., Notes on Numerical
Fluid Mechanics, 59, Vieweg Publ., Braunschweig, 1997,
pp. 113.
 M. F. Wheeler, T. Arbogast, S. Bryant,
C. N. Dawson, F. Saaf, and Chong Wang, New computational approaches
for chemically reactive transport in porous media, in Next Generation
Environmental Models and Computational Methods (NGEMCOM), Proceedings
of the U.S. Environmental Protection Agency Workshop, G. Delic and
M.F. Wheeler, eds., SIAM, Philadelphia, 1997, pp. 217226.
 T. Arbogast, M. F. Wheeler, and I. Yotov,
Logically rectangular mixed methods for flow in irregular,
heterogeneous domains, in Computational Methods in Water Resources XI,
Vol. 1, Á. A. Aldama et al., eds., Computational Mechanics
Publications, Southampton, 1996, pp. 621628.
 T. Arbogast, Mixed Methods for Flow
and Transport Problems on General Geometry, in Finite Element Modeling
of Environmental Problems, G. F. Carey, ed., Wiley, Cichester,
England, 1995, pp. 275286.
 T. Arbogast, P. T. Keenan, M. F. Wheeler,
and I. Yotov, Logically rectangular mixed methods for Darcy flow on
general geometry, SPE 29099, in Proceedings of the 13th SPE Symposium
on Reservoir Simulation held in San Antonio, Texas, Society of
Petroleum Engineers, Richardson, Texas, February 1215, 1995,
pp. 5159.
 T. Arbogast, M. F. Wheeler, and I. Yotov,
Logically rectangular mixed methods for groundwater flow and transport
on general geometry, in Computational Methods in Water Resources X,
Vol. 1, A. Peters et al., eds., Kluwer Academic Publishers, Dordrecht,
The Netherlands, 1994, pp. 149156.
 T. Arbogast, C. N. Dawson, and
M. F. Wheeler, A parallel multiphase numerical model for subsurface
contaminant transport with biodegradation kinetics, in Computational
Methods in Water Resources X, Vol. 2, A. Peters et al., eds., Kluwer
Academic Publishers, Dordrecht, The Netherlands, 1994,
pp. 14991506.
 T. Arbogast, C. N. Dawson, and
P. T. Keenan, Efficient mixed methods for groundwater flow on
triangular or tetrahedral meshes, in Computational Methods in Water
Resources X, Vol. 1, A. Peters et al., eds., Kluwer Academic
Publishers, Dordrecht, The Netherlands, 1994, pp. 310.
 T. Arbogast and
M. F. Wheeler, A parallel numerical model for subsurface contaminant
transport with biodegradation kinetics, in The Mathematics of Finite
Elements and Applications VIII (MAFELAP 1993), J. R. Whiteman, ed.,
Wiley, New York, 1994, pp. 199213.
 T. Arbogast, A simplified
dualporosity model for twophase flow, in Computational Methods in
Water Resources IX, Vol. 2: Mathematical Modeling in Water Resources,
T. F. Russell et al., eds., Computational Mechanics Publications,
Southampton, U.K., 1992, pp. 419426.
 T. Arbogast, M. Obeyesekere, and
M. F. Wheeler, Simulation of flow in rootsoil systems, in
Computational Methods in Water Resources IX, Vol. 2: Mathematical
Modeling in Water Resources, T. F. Russell et al., eds., Computational
Mechanics Publications, Southampton, U.K., 1992, pp. 195202.
 T. Arbogast, A. Chilakapati, and
M. F. Wheeler, A characteristicmixed method for contaminant transport
and miscible displacement, in Computational Methods in Water Resources
IX, Vol. 1: Numerical Methods in Water Resources, T. F. Russell et
al., eds., Computational Mechanics Publications, Southampton, U.K.,
1992, pp. 7784.
 T. Arbogast, Gravitational
forces in dualporosity models of single phase flow, in Proceedings,
Thirteenth IMACS World Congress on Computation and Applied
Mathematics, Trinity College, Dublin, Ireland, July 2226, 1991,
pp. 607608.
 T. Arbogast, M. Obeyesekere, and
M. F. Wheeler, Convergence analysis for simulating flow in rootsoil
systems, in The Mathematics of Finite Elements and Applications VII
(MAFELAP 1990), J. R. Whiteman, ed., Academic Press, London, 1991,
pp. 361383.
 T. Arbogast, J. Douglas, Jr., and
U. Hornung, Modeling of naturally fractured reservoirs by formal
homogenization techniques, in Frontiers in Pure and Applied
Mathematics, R. Dautray, ed., Elsevier, Amsterdam, 1991, pp. 119.
 P. J. Paes Leme, J. Douglas, Jr.,
T. Arbogast, and N. P. Nunes, A tall block model for immiscible
displacement in naturally fractured reservoirs, SPE 21104, in
Proceedings, Society of Petroleum Engineers Latin American Petroleum
Engineering Conference, Rio de Janeiro, Brazil, October 1519,
1990.
 J. Douglas, Jr., T. Arbogast, and
P. J. Paes Leme, Two models for the waterflooding of naturally
fractured reservoirs, Paper SPE 18425, in Proceedings, Tenth SPE
Symposium on Reservoir Simulation, Society of Petroleum Engineers,
Dallas, 1989, pp. 219225.
 T. Arbogast, J. Douglas, Jr., and
J. E. Santos, Twophase immiscible flow in naturally fractured
reservoirs, in Numerical Simulation in Oil Recovery, M. F. Wheeler,
ed., The IMA Volumes in Mathematics and its Applications, 11,
SpringerVerlag, 1988, pp. 4766.
 T. Arbogast, The double porosity
model for single phase flow in naturally fractured reservoirs, in
Numerical Simulation in Oil Recovery, M. F. Wheeler, ed., The IMA
Volumes in Mathematics and its Applications, 11,
SpringerVerlag, 1988, pp. 2345.
 J. Douglas, Jr., P. J. Paes Leme,
T. Arbogast, and T. Schmitt, Simulation of flow in naturally fractured
reservoirs, Paper SPE 16019, in Proceedings, Ninth SPE Symposium on
Reservoir Simulation, Society of Petroleum Engineers, Dallas, 1987,
pp. 271279.
Other Manuscripts

T. Arbogast, User's Guide to Parssim1: The Parallel Subsurface
Simulator, Single Phase, The Center for Subsurface Modeling,
Institute for Computational Engineering and Sciences, The University of
Texas at Austin, Austin, Texas, TICAM Report 9813, 1998.

T. Arbogast and J. L. Bona, Methods of Applied Mathematics, Department
of Mathematics, University of Texas, Austin, Texas, 19992008.
My mathematics home
page
My ICES home page
You can reach me at:
arbogast@ices.utexas.edu
Last updated: January 14, 2016.