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B. M. Riviere


Book

  • Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation.
    SIAM 2008.
    ISBN-10: 089871656X.
    ISBN-13: 978-0-898716-56-6
    Available at SIAM. Part of SIAM Bestsellers in Summer 2009.

    • Refereed Publications (Revues avec comite de lecture)

    1. B. Riviere and X. Yang. "Convergence Analysis Of A Coupled Method for Time-Dependent Convection-Diffusion Equations", Numerical Methods for Partial Differential Equations, to appear, 2013.
    2. V. Girault, G. Kanschat and B. Riviere. "Error analysis for a monolithic discretization of coupled Darcy and Stokes problems", Journal of Numerical Mathematics, to appear, also IMA preprint 2390.
    3. K. Liu and B. Riviere. "Discontinuous Galerkin Methods for Elliptic Partial Differential Equations with Random Coefficients", International Journal of Computer Mathematics, to appear.
    4. J. Young, B. Riviere, K. Uray, C. Cox. "A mathematical model of intestinal edema formation", Mathematical Medicine & Biology, to appear; doi:10.1093/imammb/dqs025.
    5. A. Cesmelioglu, V. Girault, B. Riviere. "Time-dependent coupling of Navier-Stokes and Darcy flows", ESAIM: Mathematical Modelling and Numerical Analysis, 47 (2), p. 539-554, 2013. pdf.
    6. Keyes et al. "Multiphysics Simulations: Challenges and Opportunities", International Journal of High Performance Computing Applications, 27 (1) p.4--83, 2013.
    7. A. Cesmelioglu and B. Riviere. "Existence of a weak solution for the fully coupled Navier-Stokes/Darcy-Transport problem", Journal of Differential Equations, 252, p. 4138-4175, 2012, also technical report TR10-23: pdf.
    8. P. Chidyagwai and B. Riviere. "A two-grid method for coupled free flow with porous media flow", Advances in Water Resources, 34 p.1113-1123, 2011, also technical report TR10-21, doi:10.1016/j.advwatres.2011.04.010, pdf.
    9. B. Riviere and N. Walkington. "Convergence of a discontinuous Galerkin method for the miscible displacement under low regularity", SIAM Journal on Numerical Analysis, 49, p. 1085-1110, 2011, also technical report TR09-18: pdf.
    10. P. Chidyagwai, I. Mishev and B. Riviere. "On the coupling of finite volume and discontinuous Galerkin method for elliptic problems", Journal of Computational and Applied Mathematics, 231 p.2193-2204, 2011, doi:10.1016/j.cam.2010.10.017, also technical report TR10-10: pdf.
    11. T. Wihler and B. Riviere. "Discontinuous Galerkin methods for second-order elliptic PDE with low-regularity solutions", Journal of Scientific Computing, 46 (2), p. 151-165, 2011: pdf.
    12. G. Kanschat and B. Riviere. "A strongly conservative finite element method for the coupling of Stokes and Darcy flow", Journal of Computational Physics, 229 (17), p. 5933-5943, 2010, doi 10.1016/j.jcp.2010.04.021, pdf.
    13. P. Chidyagwai and B. Riviere. "Numerical Modelling of Coupled Surface and Subsurface Flow Systems", Advances in Water Resources, 33, p.92-105, 2010 : doi:10.1016/j.advwatres.2009.10.012, pdf.
    14. J. Proft and B. Riviere. "Discontinuous Galerkin Methods for Convection-Diffusion Equations with varying and vanishing diffusivity", International Journal of Numerical Analysis and Modeling, 6 (4), p.533-561, 2009: pdf
    15. P. Chidyagwai and B. Riviere. "On the solution of the coupled Navier-Stokes and Darcy equations", Computer Methods in Applied Mechanics and Engineering, 198, p. 3806-3820, 2009, (doi:10.1016/j.cma.2009.08.012): pdf.
    16. V. Girault and B. Riviere. "DG approximation of coupled Navier-Stokes and Darcy equations by Beaver-Joseph-Saffman interface condition", SIAM Journal on Numerical Analysis, 47, p. 2052-2089, 2009, (also technical report TR-MATH 07-09 2007).
    17. A. Cesmelioglu and B. Riviere. "Primal Discontinuous Galerkin Methods For Time-Dependent Coupled Surface And Subsurface Flow", Journal of Scientific Computing, 40, p.115-140, 2009 (doi 10.1007/s10915-009-9274-4).
    18. J. Guzman and B. Riviere. "Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations", Journal of Scientific Computing, 40, p. 273-280, 2009 (doi 10.1007/s10915-008-9255-z).
    19. Y. Epshteyn, T. Khan and B. Riviere. "Numerical Solution Of A One-Dimensional Inverse Problem By The Discontinuous Galerkin Method", Mathematics and Computers in Simulation, 79 p. 1989-2000, 2009, (doi:10.1016/j.matcom.2008.08.002). This paper was the eighth most successful IMACS 2009 paper published in Mathematics and Computers in Simulation.
    20. Y. Epshteyn and B. Riviere. "Analysis of hp Discontinuous Galerkin Methods for Incompressible Two-Phase Flow", Journal of Computational and Applied Mathematics, 225 p. 487-509, 2009 (also technical report TR-MATH 06-17 2006).
    21. B. Riviere, Y. Epshteyn, D. Swigon and Y. Vodovotz. "A Simple Mathematical Model of Signaling Resulting from the Binding of Lipopolike Receptor 4 Demonstrates Inherent Preconditioning Behavior", Mathematical Biosciences, 217 (1) p. 19-26, 2009 (doi:10.1016/j.mbs.2008.10.002).
    22. A. Cesmelioglu and B. Riviere. "Analysis of time-dependent Navier-Stokes flow coupled with Darcy flow", Journal of Numerical Mathematics, 16 (4) p. 249-280, 2008.
    23. Y. Epshteyn and B. Riviere. "Convergence of high order methods for miscible displacement", International Journal of Numerical Analysis and Modeling, 5 p.47-63, 2008, pdf.
    24. Q. Mi, D. Swigon, B. Riviere, S. Cetin, Y. Vodovotz, D. Hackam. "One-dimensional elastic continuum model of enterocyte layer migration", Biophysical Journal, 93, p. 3745-3752, 2007.
    25. Q. Mi, B. Riviere, G. Clermont, D.L. Steed, Y. Vodovotz, "Agent-based modeling of inflammation and wound healing: insights into diabetic foot ulcer pathology and the role of transforming growth factor-beta 1", Wound Repair and Regeneration, 15 (5), p. 671-682, 2007. pdf.
    26. B. Riviere, S. Shaw and J.R. Whiteman. "Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity", Numerical Methods for Partial Differential Equations, 23 (5), p. 1149-1166, 2007.
    27. Y. Epshteyn and B. Riviere. "Estimation of penalty parameters for symmetric interior penalty Galerkin methods", Journal of Computational and Applied Mathematics, 206 p.843-872, 2007, (doi: 10.1016/j.cam.2006.08.029) pdf.
    28. Y. Epshteyn and B. Riviere. "Fully Implicit Discontinuous Finite Element Methods for Two-Phase Flow", Applied Numerical Mathematics, 57, p.383-401, 2007. This paper was the fourth most successful IMACS 2007 paper published in Applied Numerical Mathematics.
    29. S. Kaya, W. Layton and B. Riviere. "Subgrid Stabilized Defect Correction Methods for the Navier-Stokes Equations", SIAM Journal on Numerical Analysis, 44 (4) p.1639-1654, 2006.
    30. B. Riviere and S. Shaw. "Discontinuous Galerkin finite element approximation of nonlinear non-Fickian diffusion in viscoelastic polymers", SIAM Journal on Numerical Analysis, 44 no 6, p.2650-2670, 2006, pdf, (also technical report BICOM 04/03)
    31. W. Klieber and B. Riviere. "Adaptive simulations of two-phase flow by discontinuous Galerkin methods", Computer Methods in Applied Mechanics and Engineering, 196 p.404-419, 2006, pdf.
    32. Y. Epshteyn and B. Riviere. "On the solution of incompressible two-phase flow by a p-version discontinuous Galerkin method", Communications in Numerical Methods in Engineering, 22 p.741-751, 2006, pdf.
    33. B. Riviere and V. Girault. "Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces", Computer Methods in Applied Mechanics and Engineering, 195 p.3274-3292, 2006, online.
    34. S. Kaya and B. Riviere. "A two-grid stabilization method for solving the steady-state Navier-Stokes equations", Numerical Methods for Partial Differential Equations, 22 no 3, p. 728-743, 2006, also TR-MATH 04-06, pdf.
    35. V. Girault, B. Riviere and M. Wheeler. "A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations", Mathematical Modelling and Numerical Analysis (M2AN), 39 no 6, p. 1115-1148, 2005, also TR-MATH 04-08, pdf.
    36. S. Kaya and B. Riviere. "A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations", SIAM Journal on Numerical Analysis, 43 no 4, p. 1572-1595, 2005: also technical report TR-MATH 03-14 (2003), University of Pittsburgh: pdf.
    37. B. Riviere. "Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems", Journal of Scientific Computing, 22 no 1 p. 479-500, 2005, pdf .
    38. B. Riviere and I. Yotov. "Locally conservative coupling of Stokes and Darcy flows", SIAM Journal on Numerical Analysis, 42 no 5, p. 1959-1977, 2005: pdf.
    39. V. Girault, B. Riviere and M.F. Wheeler. "A Discontinuous Galerkin Method with Non-Overlapping Domain Decomposition for the Stokes and Navier-Stokes Problems", Mathematics of Computation, 74, p. 53-84, 2005, pdf .
    40. B. Riviere. "Analysis of a multi-numerics/multi-physics problem", in Numerical Mathematics and Advanced Applications, pp. 726--735, Springer-Verlag 2004. postscript.
    41. P. Bastian and B. Riviere. "Superconvergence and H(div) Projection for Discontinuous Galerkin Methods", International Journal for Numerical Methods in Fluids, Volume 42 p. 1043-1057, 2003.
    42. B. Riviere and M.F. Wheeler. "A Posteriori Error Estimates and Mesh Adaptation Strategy for Discontinuous Galerkin Methods Applied to Diffusion Problems" Computers & Mathematics with Applications , Volume 46, Number 1 p. 141-163, 2003: pdf.
    43. B. Riviere and M.F. Wheeler. "Discontinuous Finite Element Methods for Acoustic and Elastic Wave Problems" Contemporary Mathematics, volume 329, pp. 271--282, 2003. postscript.
    44. B. Riviere, S. Shaw, M.F. Wheeler and J.R. Whiteman. "Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity", Numerische Mathematik, Volume 95, Number 2 p. 347-376, 2003 pdf
    45. E.W. Jenkins; B. Riviere and M.F. Wheeler. "A Priori Error Estimates for Mixed Finite Element Approximations of the Acoustic Wave Equation". SIAM Journal on Numerical Analysis , pdf , Volume 40, Number 5 p. 1698-1715, 2002.
    46. B. Riviere and M.F. Wheeler. "Coupling Locally Conservative Methods for Single Phase Flow", Computational Geosciences, Volume 6 number 3 p. 269-284, 2002: pdf
    47. S. Sun, B. Riviere and M.F. Wheeler. "A combined mixed finite element and discontinuous Galerkin method for miscible displacement problem in porous media". Recent Progress in Computational and Applied PDEs, Kluwer/Plenum, New York, pp.323--348, 2002: pdf
    48. B. Riviere and M.F. Wheeler. "Non Conforming Methods for Transport with Nonlinear Reaction". Contemporary Mathematics, volume 295, pp 421-432, 2002. pdf.
    49. B. Riviere and M.F. Wheeler. "Discontinuous Galerkin Methods for Flow and Transport Problems in Porous Media", Communications in Numerical Methods in Engineering , 18 p. 63-68 (2002). pdf .
    50. B. Riviere; M.F. Wheeler and V. Girault. "A Priori Error Estimates for Finite Element Methods based on Discontinuous Approximation Spaces for Elliptic Problems" SIAM Journal on Numerical Analysis, volume 39 number 3 (2001) p. 902-931. pdf.
    51. B. Riviere; M.F. Wheeler and K. Banas. " Part II. Discontinuous Galerkin Method Applied to Single Phase Flow in Porous Media", Computational Geosciences, volume 4 number 4, p. 337-341 (2000). pdf .
    52. B. Riviere and M.F. Wheeler. "Locally conservative algorithms for flow" MAFELAP 1999 Proceedings, pp 29-46, 2000.
    53. B. Riviere; M.F. Wheeler and V. Girault. "Improved Energy Estimates for Interior Penalty, Constrained and Discontinuous Galerkin Methods for Elliptic Problems. Part I". Computational Geosciences , volume 8, p. 337-360, April 1999. pdf .
    54. B. Riviere and M.F. Wheeler. "A discontinuous Galerkin methods applied to nonlinear parabolic equations". Discontinuous Galerkin Methods: Theory, Computation and Applications, volume 11, p. 231-244, July 1999.
    55. G.Baker, J. Gunnels, G. Morrow, B. Riviere, R. Van De Geijn. "PLAPACK: High performance through high level abstraction". Proceedings of the 1998 International Conference on Parallel Processing, 1998. pdf .

    Preprints

    1. B. Riviere and S. Sardar. "Penalty-free discontinuous Galerkin methods for incompressible Navier-Stokes equations", submitted, also technical report TR12-09, 2012.
    2. S. Ozisik, B. Riviere and T. Warburton. "On the constants in inverse inequalities in L2", submitted, also technical report TR10-19.

      3. CAAM technical reports are found here

    Some selected publications

    1. V. Girault, G. Kanschat and B. Riviere. "On the coupling of incompressible Stokes or Navier-Stokes and Darcy flows through porous media". In book "Modelling and Simulation in Fluid Dynamics in Porous Media", ed. Ferreira, Barbeiro, Pena, Wheeler, Conference proceedings, 2012.
    2. J. Young and B. Riviere. "The development of a computational, poroelastic model of intestinal edema". Proceedings of the ECCOMAS Thematic International Conference on Simulation and Modeling of Biological Flows (SIMBIO 2011) September 21--23, 2011, VUB, Brussels, Belgium.
    3. B. Riviere, P. Chidyagwai, I. Mishev, "On the coupling of finite volume and discontinuous Galerkin for reservoir simulation problems". Proceedings of the SPE conference, 2011.
    4. Y. Epshteyn and B. Riviere, "Fully implicit discontinuous Galerkin scheme for two-phase flow". Proceedings of the MSRI workshop "The Legacy of Ladyzhenskaya and Oleinik", 2006.
    5. Y. Vodovotz et al. Mathematical simulations of sepsis and trauma, Proceedings of the 11th Congress of the European Shock Society, pp. 151-159, 2005.
    6. B. Riviere. "Numerical study of a discontinuous Galerkin method for incompressible two-phase flow", ECCOMAS Proceedings, 2004.
    7. M.F. Wheeler, M. Peszynska and B. Riviere. "Computational science issues in modeling oil and gas production". Proceedings of the 8th European Conference on the Mathematics of Oil Recovery- ECMOR VIII, publisher European Association of Geoscientists and Engineers (EAGE), 2002.
    8. M.F. Wheeler, S. Sun, O. Eslinger and B. Riviere, "Discontinuous Galerkin method for modeling flow and reactive transport in porous media". In Wendland (ed), Analysis and Simulation of Multifield Problem, Springer-Verlag, pp. 37-58.
    9. B. Riviere; E. Jenkins. "In Pursuit of Better Models and Simulations, Oil Industry Looks to the Math Sciences". SIAM News, January/February 2002.
    10. B. Riviere and M.F. Wheeler. "Miscible displacement in porous media". In Computational Methods in Water Resources, Developments in Water Science, Hassanizadeh S.M., Schotting R.J., Gray W.G., Pinder G.F. (eds), Elsevier, pp 907-914, 2002. postscript, pdf.
    11. M. Guillot, B. Riviere and M.F. Wheeler. "Discontinuous Galerkin methods for mass conservation equations for environmental modeling". In Computational Methods in Water Resources, Developments in Water Science, Hassanizadeh S.M., Schotting R.J., Gray W.G., Pinder G.F. (eds), Elsevier, pp 939-946, 2002. postscript, pdf.
    12. E. Jenkins; B. Riviere. "Geoscientists Meet in Colorado to Explore Increasingly Complex, Multidisciplinary Problems", SIAM News, 24 (9) November 2001.
    13. B. Riviere, M.F. Wheeler and E. Jenkins. "Locally conservative algorithms for flow". Proceedings of the Department of Defence User's Group Conference, 2001.
    14. C. Dawson; B. Riviere and M.F. Wheeler. "Discontinuous Galerkin Methods for Flow and Reactive Transport". Proceedings of the Department of Defense. User's Group Conference, Albuquerque, June 5-8, 2000 (available on CD-ROM).

    Some technical reports

    1. A. Cesmelioglu and B. Riviere. "Analysis of weak solutions for the fully coupled Stokes-Darcy-Transport problem", technical report TR09-38.
    2. J. Proft and B. Riviere. "Analytical and numerical study of diffusive fluxes for transport equations with near-degenerate coefficients". TR-MATH 06-07, Pittsburgh, 2006.
    3. B. Riviere. "The DGIMPES Model in IPARS: Discontinuous Galerkin for Two-Phase Flow Integrated in a Reservoir Simulator Framework". TICAM Report 02-29, Austin 2002.
    4. M. Guillot, B. Riviere and M.F. Wheeler. "An Implementation of a Discontinuous Galerkin Discretization of the Mass Conservation Equations in CEQUAL-ICM". TICAM Report 02-13, Austin 2002.
    5. B. Riviere and M.F. Wheeler. "Discontinuous Finite Element Methods for Acoustic and Elastic Wave Problems. Part I: Semidiscrete Error Estimates", TICAM Report 01-02, Austin, 2001.
    6. B. Riviere and M.F. Wheeler. "Optimal Error Estimates for Discontinuous Galerkin Methods Applied to Linear Elasticity Problems", TICAM Report 00-30, Austin, 2000.
    7. B. Riviere; K. Banas and M.F. Wheeler. "hp 3D Flow Simulations with Discontinuous Galerkin Methods", TICAM Report 00-29, Austin, 2000.
    8. B. Riviere and M.F. Wheeler. "A Posteriori Error Estimates and Mesh Adaptation Strategy for Discontinuous Galerkin Methods Applied to Diffusion Problems", TICAM Report 00-10, Austin, 2000.
    9. B. Riviere; M.F. Wheeler and C. Baumann. "Part II. Discontinuous Galerkin Method Applied to a Single Phase Flow in Porous Media", TICAM Report 99-10, Austin, 1999.

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