Jean-Luc Guermond
Professor

Education

• Habilitation Dissertation, Mathematics, University of Paris VI, France, 1995
• French Aggregation, Mathematics, University of Paris VI, France, 1990
• Ph.D, Theoretical Mechanics, University of Paris VI, France, 1985
• M.S., Theoretical Mechanics, University of Paris VI, France, 1983

In the Profession

• 2004-present, Professor, Department of Mathematics, Texas A&M
• 2001-2003, Visiting professor, ICES, UT Austin, TX
• 1990-2001, CNRS Research Scientist at LIMSI, Orsay, France
• 1987-1990, Research Associate at Bassin d'Essais de Carenes, Paris, France
• 1986-1987, Post-Doc, Department of Ocean Engineering, MIT, Boston, MA
• 1984-1986, Research Associate at Bassin d'Essais de Carenes, Paris, France

Research or Scholarly Interests

1) Numerical Analysis: Finite element approximation, Discontinuous Galerkin methods, Stabilization, Multi-scale approximations, Homogenization.

2) Partial Differential Equations: Navier-Stokes equations (From smoothness questions in 3D to Approximation), Magneto-hydodynamics, Maxwell equations, Transport equations, Conservation laws, Hamilton-Jacobi equations.

Major Awards

• 2001-2003, ICES Fellowship.

Notable Recent Grants

•  AFOSR, L1-Based approximations for PDEs and Applications, PI, April 2009-April 2011.
• US DOE (C09-00035) 09 Sep 2008 to 30 June 2011, ``Support of Stockpile Stewardship Program'', Co-PI.
• NSF-DMS (0811041), July 2008 to June 2011, ``L1-based Approximation Techniques for PDEs'', Co-PI.
• NSF-DMS (0713829), Aug 2007 to Aug 2010, ``Discontinuous Galerkin Methods for PDEs with Heterogeneous Coefficients'', PI.
• US DOE (C08-00358), Sept 07 to Sept 08, ``High Fidelity 3-D Core Model for Light Water Reactor Nuclear Reactors'', Co-PI.
• NSF-DOE (07-545), ``Framework for Developing Novel Detection Systems
  Focused on Interdicting Shielded HEU'', Co-PI.
•  NFS-DMS (0510650), June 2005 to May 2008,
  "Nonlinear finite element approximation of first-order PDE's in L1", PI.
• NFS, DGE - IGERT (0523626):  (2005-2010) "IGERT: New Mathematical Tools for Next Generation Materials", Co-PI.

Five Selected Publications or Scholarly Works

• J.-.L. Guermond, B. Popov, An optimal L1-minimization algorithm for stationnary
  Hamilton-Jacobi equations, Commications in Mathematical Sciences, 7:1 (2009), 211-238.
• J.-L. Guermond, R. Laguerre, J. Leorat, C. Nore, A solution method for nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a Fourier/Finite Element technique and an Interior Penalty Method, J. Comput. Phys. 228 (2009) 2739-2757.
• J.-.L. Guermond, J. Pasciak, Stability of Discrete Stokes operators in fractional Sobolev Spaces, Journal of Mathematical Fluid Mechanics, 10 (2008) 588-610
• Ern, J.-.L. Guermond, Discontinuous Galerkin Methods for Friedrichs' Systems. Part III. Multi-field theories with partial coercivity, SIAM J. Numer. Anal., 46:2 (2008) 776-804.
• J.-.L. Guermond, Faedo-Galerkin weak solutions of the Navier--Stokes equations
  with Dirichlet boundary conditions are suitable, Journal de Mathematiques Pures et Appliquees, 88 (2007) 87-106.

Recent Synergistic Activities

• Coordinator of the Numerical Analysis seminar 2005-2008.

Recent Graduate Students and/or Postdocs

• Mentored two Postdocs:  
• Francois Marpeau, Post-Doc, Texas A&M, (2005-2006).
• Vesselin Dobrev, Post-Doc, Texas A&M, (2007-2009).
• Abner Salgado, PhD. Graduate, Texas A&M, (2006-).
• Raphael Laguerre, PhD Graduate (Univ. Paris VII), (2003-2006); Co-advising.
• Adolfo Ribeiro, PhD Graduate (Univ. Paris XI), (2006-2009); Co-advising. 
• Franky Luddens, PhD Graduate (Univ. Paris XI), (2009-); Co-advising.
• Chaired 1 master student committee last 5 years.