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Beatrice Riviere
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Research Group: from left to right: Kun Liu, Xin Yang, Jizhou Li, Jun Tan, Richard Rankin

POSTDOCTORAL FELLOWS

  • Richard Rankin. Multiphase multicomponent. In progress.
  • Jennifer Young. Mathematical modeling of intestinal edema using a poroelastic inhomogeneous model. 2010-2012. Jennifer was a bright young mathematician, whose life was accidently taken by a moving car on Main Street.

    • STUDENTS

    Ph.D. students

  • Jun Tan. Poroelasticity. In progress.
  • Jizhou Li. High order methods for miscible displacement. In progress.
  • Xin Yang. Multinumeric method for CO2 storage. In progress.
  • Kun Liu. PhD 2013. "Discontinuous Galerkin methods for parabolic partial differential equations with random input data". Research partially funded by NSF. Kun is currently an employee of a company in oil reservoir management.
  • Sevtap Ozisik. Ph.D. 2012 from Middle East Technical University, Turkey. "Fully Computable Convergence Analysis of Discontinuous Galerkin Finite Element Approximation with an Arbirtrary Number of Levels of Hanging Nodes. Sevtap is currently a Postdoctoral Research Assistant at METU.
  • Aycil Cesmelioglu. PhD 2010. "Complex Flow and Transport Phenomena in Porous Media". Research partially funded by NSF. Aycil is currently an Assistant Professor at Oakland University.
  • Prince Chidyagwai. PhD 2010. "Coupling Surface Flow with Porous Media Flow". Research partially funded by NSF. Prince is currently an Assistant Professor of Research at Temple University.
  • Qi Mi. PhD 2007. "Modeling The Wound Healing In Necrotizing Enterocolitis And Diabetic Foot Ulcer". Joint supervision with David Swigon. Research partially funded by NIH. Currently Assistant Professor in the School of Health and Medicine at University of Pittsburgh.
  • Yekaterina Epshteyn. PhD 2007. "Hp Primal Discontinuous Galerkin Finite Element Methods For Two-Phase Flow In Porous Media". Research partially funded by NSF and NIH. Currently, Assistant Professor in the department of Mathematics at University of Utah.
  • Songul Kaya. PhD 2004. "Numerical Analysis of a Variational Multiscale Method". Joint supervision with William Layton. Winner of the 2004 Hales Distinguished Research Award for the best doctoral dissertation. Currently, Associate Professor at Middle East Technical University, Turkey.

    • Master students

  • Shirin Sardar. M.A. 2012. "Penalty-Free Discontinuous Galerkin Methods for the Stokes and Navier-Stokes Equations".
  • Xin Yang. M.A. 2012. "A Coupled Finite Volume and Discontinuous Galerkin Method for Convection-Diffusion Problems".
  • Toni Tullius. M.A. 2011. "Accelerated Discontinuous Galerkin Solvers with the Chebyshev Iterative Method on the Graphics Processing Unit". Joint supervision with Tim Warburton.
  • Kun Liu. M.A. 2010. "Discontinuous Galerkin Methods for Elliptic Partial Differential Equations with Random Coefficients".
  • Christina Ho. M.A. 2010. "Discontinuous Galerkin Formulation for Multi-component Multiphase Flow". Currently at El Paso company in Houston.
  • Ahmet Izmirlioglu. M.S. 2008. "Numerical and theoretical studies of high order methods".
  • Michael Chiacchiero. M.S. 2007. "Efficient PETSc Solvers for Discontinuous Galerkin Methods Applied to Elliptic Problems". Currently math professor at Edison State College.

    • Undergraduate students

  • Rebecca McKinnell. 2013. Research funded by NSF.
  • Justin Dong. 2013. Research funded by NHARP.
  • Joey Huchette. 2011. Research funded by NHARP.
  • Yichen Lu. 2011. Research funded by NHARP.
  • John Vogelgesang. 2011. Research funded by NHARP.
  • Yuekai Sun. 2009. Research funded by a Brown Undergraduate Research Internship and a NSF grant. Yuekai is currently a Ph.D. student at Stanford University.
  • William Klieber. Bachelor of Philosophy thesis, 2006. "Numerical Simulations of Two-Phase Flow". Research funded by CDRF (Spring 2004) and a Brackenridge Fellowship (Summer 2004). Currently, graduate student in Computer Science department at Carnegie Mellon University.

    • RESEARCH INTERESTS top

    Numerical Analysis of Discontinuous Galerkin (DG) Finite Element Methods:
    I am mostly interested in the primal DG methods such as NIPG, SIPG or IIPG.

  • Elliptic equations with discontinuous coefficients
  • Parabolic equations: with or without convection term, with degenerate diffusion
  • Linear equations: elasticity, quasi-static and dynamic viscoelasticity equations, acoustic and elastic wave problem
  • Nonlinear equations: Navier-Stokes equations, miscible displacement, two-phase flow, three-phase flow, nonlinear non-Fickian diffusion in viscoelastic polymers
  • A posteriori error estimation
  • Slope limiters on unstructured nonconforming meshes

    • Multiphase Flow: Simulations and Analysis
    Two-phase flow: Sequential approach v. fully coupled approach, mesh and time adaptivity, DG methods, 2D/3D simulations, gravity, well models.
    Three-phase flow

    Incompressible Flow: Simulations and Analysis
    Stokes equations, Navier-Stokes equations, subgrid eddy viscosity turbulence model, DG method and classical finite element methods (FEM).

    Multi-numerics and/or Multi-physics Approach

  • Coupling of Stokes and Darcy using DG
  • Coupling of steady-state Navier-Stokes and Darcy using DG
  • Coupling of time-dependent Navier-Stokes and Darcy using DG
  • Coupling of time-dependent Navier-Stokes and Darcy using FEM
  • Coupling of DG and MFE for single phase flow (elliptic problem)
  • Coupling of DG with MFE for coupled Stokes and Darcy
  • Coupling of DG with FEM for coupled steady-state Navier-Stokes and Darcy

    • Bio-Medical Applications

  • Modeling of intestinal edema
  • Modeling of myosin light chain phosphorylation
  • Modeling of cell migration in Necrotizing Enterocolitis
  • Modeling of binding of LPS with TLR4 and signaling cascade

    • Miscible Displacement Problem

  • Convergence of backward Euler in time with high order DG in space
  • Convergence of DG in time with mixed finite element (MFE) in space
  • Numerical simulation for unstable flow

    • Other Applications

  • Single phase flow: highly discontinuous permeability, fractures
  • Acoustic wave propagation: DG, MFE
  • Optical tomography inverse problem: DG

    • EDITORIAL BOARD top

  • Advances in Water Resources
  • International Journal of Computer Mathematics
  • SIAM Journal on Numerical Analysis

    • CURRENT COLLABORATORS

  • Ivo Babuska, University of Texas at Austin
  • Vivette Girault, Laboratoire Jacques-Louis Lions, Universite Paris VI
  • Johnny Guzman, Brown University
  • Guido Kanschat, Texas A&M University
  • Ilya Mishev, ExxonMobil
  • Jennifer Proft, University of Texas at Austin
  • Yoram Vodovotz, University of Pittsburgh
  • Noel Walkington, Carnegie Mellon University
  • Thomas Wihler, University of Bern

    • Useful Links

  • IMA
  • MathSciNet
  • NA Digest



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