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

  1. T. Arbogast and M. R. Correa. Two families of H(div) mixed finite elements on quadrilaterals of minimal dimension, submitted.
  2. T. Arbogast and A. L. Taicher. A linear degenerate elliptic equation arising from two-phase mixtures, submitted.
  3. Ch.-S. Huang and T. Arbogast. An Eulerian-Lagrangian WENO scheme for nonlinear conservation laws, submitted.
  4. Ch.-S. Huang, T. Arbogast, and Ch.-H. Hung. A semi-Lagrangian finite difference WENO scheme for scalar nonlinear conservation laws, submitted.

Publications in Journals and Other Refereed Works

  1. 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. 169-198.
  2. T. Arbogast and Hailong Xiao. Two-level mortar domain decomposition preconditioners for heterogeneous elliptic problems, Comput. Methods Appl. Mech. Engrg., 292 (2015), pp. 221-242.
  3. Ch.-S. Huang, F. Xiao, and T. Arbogast, Fifth order multi-moment WENO schemes for hyperbolic conservation laws, J. Sci. Comput., 2014, to appear.
  4. Ch.-S. Huang, T. Arbogast, Ch.-H. Hung, A re-averaged WENO reconstruction and a third order CWENO scheme for hyperbolic conservation laws, J. Comput. Phys. 262 2014, pp. 291-312.
  5. T. Arbogast and M. Juntunen and J. Pool and M. F. Wheeler, A discontinuous Galerkin method for two-phase flow in a porous medium enforcing H(div) velocity and continuous capillary pressure, Comput. Geosci. 17:6 (2013), pp. 1055-1078.
  6. T. Arbogast, D. Estep, B. Sheehan, and S. Tavener. A-posteriori error estimates for mixed finite element and finite volume methods for problems coupled through a boundary with non-matching grids, IMA J. Numer. Anal. 34 (2014), pp. 1625-1653.
  7. 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. 377-399.
  8. 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. 9-21.
  9. Reprint: T. Arbogast, Ch.-S. Huang, and Ch.-H. Hung, A fully conservative Eulerian-Lagrangian stream-tube method for advection-diffusion problems, SIAM J. Sci. Comput., 34:4 (2012), pp. B447-B478
  10. Reprint: T. Arbogast, Ch.-S. Huang, and T. F. Russell, A locally conservative Eulerian-Lagrangian method for a model two-phase flow problem in a one-dimensional porous medium, SIAM J. Sci. Comput., 34:4 (2012), pp. A1950-A1974.
  11. Ch.-S. Huang, T. Arbogast, and Jianxian Qiu, An Eulerian-Lagrangian WENO finite volume scheme for advection problems, J. Comp. Phys, 231:11 (2012), pp. 4028-4052. DOI 10.1016/j.jcp.2012.01.030
  12. 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. 1549-1573.
  13. 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 978-3-642-22060-9.
  14. Reprint: T. Arbogast, Homogenization-Based Mixed Multiscale Finite Elements for Problems with Anisotropy, Multiscale Modeling and Simulation 9:2 (2011), pp. 624-653.
  15. 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. 797--823.
  16. T. Arbogast and Ch.-S. Huang, A fully conservative Eulerian-Lagrangian method for a convection-diffusion problem in a solenoidal field, J. Comput. Phys. 229 (2010), pp. 3415--3427.
  17. Jichun Li, T. Arbogast, and Yunqing Huang, Mixed methods using standard conforming finite elements, Comp. Meth. in Appl. Mech. and Engng. 198(2009), pp. 680-692.
  18. T. Arbogast and M. S. M. Gomez, A discretization and multigrid solver for a Darcy-Stokes system of three dimensional vuggy porous media, Computational Geosciences 13 (2009), pp. 331-348. DOI 10.1007/s10596-008-9121-y
  19. R. Naimi-Tajdar, 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).
  20. 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. 319-346.
  21. T. Arbogast and D. S. Brunson, A computatonal method for approximating a Darcy-Stokes system governing a vuggy porous medium, Computational Geosciences, 11(3) (2007), pp. 207-218.
  22. Reprint: T. Arbogast, Ch.-S. Huang, and S.-M. Yang, Improved accuracy for alternating-direction methods for parabolic equations based on regular and mixed finite elements, Mathematical Models & Methods in Applied Sciences 17 (2007), pp. 1279-1305
  23. T. Arbogast and Chieh-Sen Huang, A fully mass and volume conserving implementation of a characteristic method for transport problems, SIAM J. Sci. Comput. 28 (2006), pp. 2001-2022.
  24. T. Arbogast and H. L. Lehr, Homogenization of a Darcy-Stokes system modeling vuggy porous media, Computational Geosciences, 10 (2006), pp. 291-302.
  25. Reprint: T. Arbogast and K. J. Boyd, Subgrid Upscaling and Mixed Multiscale Finite Elements, SIAM J. Numer. Anal., 44 (2006), pp. 1150-1171.
  26. 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. 1914-1931.
  27. Reprint: T. Arbogast, Analysis of a two-scale, locally conservative subgrid upscaling for elliptic problems, SIAM J. Numer. Anal., 42 (2004), pp. 576-598.
  28. 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. 21-32.
  29. T. Arbogast and S. L. Bryant, A Two-Scale Numerical Subgrid Technique for Waterflood Simulations, SPE J., Dec. 2002, pp. 446-457.
  30. T. Arbogast, Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow, Computational Geosciences, 6 (2002), pp. 453-48
  31. T. Arbogast, Numerical subgrid upscaling of two-phase 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. 35-49.
  32. T. Arbogast, L. C. Cowsar, M. F. Wheeler, and I. Yotov, Mixed finite element methods on non-matching multiblock grids, SIAM J. Numer. Anal., 37 (2000), pp. 1295-1315.
  33. T. Arbogast, C. N. Dawson, P. T. Keenan, M. F. Wheeler, and I. Yotov, Enhanced cell-centered finite differences for elliptic equations on general geometry, SIAM J. Sci. Comput., 19 (1998), pp. 404-425.
  34. T. Arbogast and I. Yotov, A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids, Comp. Meth. in Appl. Mech. and Engng., 149 (1997), pp. 225-265.
  35. T. Arbogast, Computational aspects of dual-porosity models, in Homogenization and Porous Media, U. Hornung, ed., Interdisciplinary Applied Math. Series, Springer, New York, 1997, pp. 203-223.
  36. T. Arbogast, M. F. Wheeler, and I. Yotov, Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences, SIAM J. Numer. Anal., 34 (1997), pp. 828-852.
  37. 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. 19-32,.
  38. T. Arbogast, M. F. Wheeler, and Nai-Ying 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. 1669-1687.
  39. T. Arbogast, C. N. Dawson, and M. F. Wheeler, A parallel algorithm for two phase multicomponent contaminant transport, Applications of Math., 40 (1995), pp. 163-174,.
  40. T. Arbogast and Zhangxin Chen, On the implementation of mixed methods as nonconforming methods for second order elliptic problems, Math. Comp., 64 (1995), pp. 943-972.
  41. T. Arbogast and M. F. Wheeler, A characteristics-mixed finite element method for advection dominated transport problems, SIAM J. Numer. Anal., 32 (1995), pp. 404-424.
  42. T. Arbogast, Gravitational forces in dual-porosity systems. II. Computational validation of the homogenized model, Transport in Porous Media, 13 (1993), pp. 205-220.
  43. T. Arbogast, Gravitational forces in dual-porosity systems. I. Model derivation by homogenization, Transport in Porous Media, 13 (1993), pp. 179-203.
  44. T. Arbogast, M. Obeyesekere, and M. F. Wheeler, Numerical methods for the simulation of flow in root-soil systems, SIAM J. Numer. Anal., 30 (1993), pp. 1677-1702.
  45. 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. 73-106.
  46. T. Arbogast, The existence of weak solutions to single-porosity and simple dual-porosity models of two-phase incompressible flow, J. Nonlinear Analysis: Theory, Methods, and Applications, 19 (1992), pp. 1009-1031.
  47. J. Douglas, Jr., J. L. Hensley, and T. Arbogast, A dual-porosity model for waterflooding in naturally fractured reservoirs, Comp. Meth. in Appl. Mech. and Engng., 87 (1991), pp. 157-174.
  48. J. Douglas, Jr., and T. Arbogast, Dual-porosity models for flow in naturally fractured reservoirs, in Dynamics of Fluids in Hierarchical Porous Media, J. H. Cushman, ed., Academic Press, London, 1990, pp. 177-221.
  49. 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. 823-836.
  50. T. Arbogast and F. A. Milner, A finite difference method for a two-sex model of population dynamics, SIAM J. Numer. Anal., 26 (1989), pp. 1474-1486.
  51. 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. 5-51.
  52. T. Arbogast, Analysis of the simulation of single phase flow through a naturally fractured reservoir, SIAM J. Numer. Anal., 26 (1989), pp. 12-29.

Publications in Unrefereed Works

  1. R. Naimi-Tajdar, 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 22-26, 2006.
  2. 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 nicht-standard Finite-Elemente-Methoden mit Anwendungen organized by K. Hackl, C. Carstensen, and D. Braess, Extended abstract, 2005.
  3. 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 26-29, 2004.
  4. T. Arbogast, D. S. Brunson, S. L. Bryant, and J. W. Jennings, Jr., A preliminary computational investigation of a macro-model for vuggy porous media, in Proceedings of the conference Computational Methods in Water Resources XV, C. T. Miller, et al., eds., Elsevier, 2004.
  5. 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 11-14, 2001.
  6. 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. 161-166, 2000.
  7. 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 14-17, 1999.
  8. 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. 453-460.
  9. T. Arbogast, S. E. Minkoff, and P. T. Keenan, An operator-based 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. 405-412.
  10. 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 8-11, 1997.
  11. 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. 1-13.
  12. 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. 217-226.
  13. 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. 621-628.
  14. 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. 275-286.
  15. 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 12-15, 1995, pp. 51-59.
  16. 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. 149-156.
  17. 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. 1499-1506.
  18. 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. 3-10.
  19. 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. 199-213.
  20. T. Arbogast, A simplified dual-porosity model for two-phase 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. 419-426.
  21. T. Arbogast, M. Obeyesekere, and M. F. Wheeler, Simulation of flow in root-soil 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. 195-202.
  22. T. Arbogast, A. Chilakapati, and M. F. Wheeler, A characteristic-mixed 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. 77-84.
  23. T. Arbogast, Gravitational forces in dual-porosity models of single phase flow, in Proceedings, Thirteenth IMACS World Congress on Computation and Applied Mathematics, Trinity College, Dublin, Ireland, July 22-26, 1991, pp. 607-608.
  24. T. Arbogast, M. Obeyesekere, and M. F. Wheeler, Convergence analysis for simulating flow in root-soil systems, in The Mathematics of Finite Elements and Applications VII (MAFELAP 1990), J. R. Whiteman, ed., Academic Press, London, 1991, pp. 361-383.
  25. 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. 1-19.
  26. 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 15-19, 1990.
  27. 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. 219-225.
  28. T. Arbogast, J. Douglas, Jr., and J. E. Santos, Two-phase 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, Springer-Verlag, 1988, pp. 47-66.
  29. 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, Springer-Verlag, 1988, pp. 23-45.
  30. 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. 271-279.

Other Manuscripts

  1. 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 98-13, 1998.
  2. T. Arbogast and J. L. Bona, Methods of Applied Mathematics, Department of Mathematics, University of Texas, Austin, Texas, 1999-2008.

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You can reach me at: arbogast@ices.utexas.edu
Last updated: January 14, 2016.