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Noel J. Walkington, Professor Ph.D., The University of Texas at Austin Email: noelw@andrew.cmu.eduOffice: Wean Hall 7117 Phone: 4122686291 Research:Walkington's research centers around the analysis of numerical schemes to approximate solutions of (systems of) partial differential equations. These equations are used ubiquitously in science and engineering to simulate virtually every macroscopic system and form the corner stone of predictive design capability. Examples include response of liquid crystals, ground flow in heterogeneous media, and plastic deformation of crystalline materials.
Algorithms to approximate the solution of partial differential equations involve mesh generation (computational geometry), (non) linear solvers (computational linear algebra), and a numerical kernel (numerical analysis). The major focus of Walkington's work is on the later component; in particular, the development of numerical schemes which faithfully inherit as many of the properties of the (partial differential) equations as possible. Tools from analysis continue to play an increasingly important role in the modeling, simulation, and understanding of complex physical systems. His research together tools from partial differential equations, continuum mechanics, and numerical analysis, to analyze numerical schemes to simulate these systems.
Selected Publications:

Walkington, N. J. and Rulla, J., "Optimal Rates of Convergence for Degenerate Parabolic Problems in Two Dimensions," SINUM, Volume 33, Number 1, February 1996, pp. 56–67.

Nicolaides, R. A. and Walkington, N. J., "Strong Convergence of Numerical Solutions to Degenerate Variational Problems," Math. Comp., Volume 64, Number 209, January 1995, pp. 117–127.

Ma, L. and Walkington, N. J., "On Algorithms for NonConvex Optimization," SIAM J. Numer. Anal. , Volume 32, Number 3, June 1995, pp. 900–923.
Recent CNA Publications:  13CNA012, High Order Schemes for Wave Equations
, Noel J. Walkington, (download paper)
 09CNA007, InfSup Conditions for Twofold Saddle Point Problems, Jason S. Howell, Noel J. Walkington, (download paper)
 03CNA023, Error Estimates for the Discontinuous Galerkin Methods for Implicit Parabolic Equations, K. Chrysafinos, Noel J. Walkington, (download paper)
 03CNA022, Error Estimates for the Discontinuous Galerkin Methods for Parabolic Equations, K. Chrysafinos, Noel J. Walkington, (download paper)
 03CNA006, Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity, Chun Liu, Noel J. Walkington, (download paper)
 03CNA005, Convergence of the Discontinuous Galerkin Methods for Discontinuous Solutions, Noel J. Walkington, (download paper)
 02CNA023, An Incremental Delaunay Meshing Algorithm, Gary L. Miller, Steven E. Pav, Noel J. Walkington, (download paper)
 02CNA015, Convergence of the Discontinuous Galerkin Method for Discontinuous Solutions, Noel J. Walkington, (download paper)
 02CNA011, An Incremental Delaunay Meshing Algorithm, Gary L. Miller, Steven E. Pav, Noel J. Walkington, (download paper)
 00CNA026, An Eulerian Description of Fluids Containing ViscoHyperelastic Particles, Chun Liu, Noel J. Walkington, (download paper)
