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B. M. Riviere


STUDENTS

Current Ph.D. students

  • Aycil Cesmelioglu. Flow in porous media. Research partially funded by NSF grant.
  • Prince Chidyagwai. Multiphysics problem. Research partially funded by NSF grant.
  • Sevtap Osizik, Ph.D. student at Middle East Technical University, Turkey. A posteriori error estimation.
  • Kun Liu. Study of uncertainty.
  • Christina Ho. Study of multiphase multicomponent flow.
  • Toni Tullius

    • Current undergraduate students

  • Yuekai Sun. Research funded by a Brown Undergraduate Research Internship and a NSF grant.

    • Past Ph.D. students

  • Qi Mi. PhD "Modeling The Wound Healing In Necrotizing Enterocolitis And Diabetic Foot Ulcer". Graduation 2007. Joint supervision with David Swigon. Research partially funded by NIH grant. Currently assistant professor in the School of Health and Medicine at University of Pittsburgh.
  • Yekaterina Epshteyn. PhD "Hp Primal Discontinuous Galerkin Finite Element Methods For Two-Phase Flow In Porous Media". Graduation 2007. Research partially funded by NSF and NIH grants. Currently postdoctoral fellow at Carnegie Mellon University (three year position funded by NSF). In 2007, Yekaterina was the most highly recruited graduate student in the department of Mathematics at the University of Pittsburgh.
  • Songul Kaya. PhD "Numerical Analysis of a Variational Multiscale Method". Graduation 2004. 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.

    • Past M.S. students

  • Ahmet Izmirlioglu. Master thesis Numerical and theoretical studies of high order methods. Graduation 2008.
  • Michael Chiacchiero. Master thesis "Efficient PETSc Solvers for Discontinuous Galerkin Methods Applied to Elliptic Problems". Graduation 2007.

    • Past undergraduate students

  • William Klieber. Bachelor of Philosophy thesis "Numerical Simulations of Two-Phase Flow", 2006. 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

    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

    • Medical Applications

  • Inflammation and sepsis: Center for Inflammation and Regenerative Modeling
  • 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

    Advances in Water Resources

    CURRENT COLLABORATORS

  • Ivo Babuska, University of Texas at Austin
  • Yekaterina Epshteyn, Carnegie Mellon University
  • Vivette Girault, Laboratoire Jacques-Louis Lions, Universite Paris VI
  • Johnny Guzman, Brown University
  • Jennifer Proft, University of Texas at Austin
  • Yoram Vodovotz, University of Pittsburgh
  • Noel Walkington, Carnegie Mellon University

    • Useful Links

  • IMA
  • MathSciNet
  • NA Digest



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