Spring 2014

ACMS 60-790-01: Numerical Analysis II

Class time: MWF 2:00 - 2:50pm.

Classroom: 105 Pasquerilla Center

Office hours: W 4:00pm - 5:00pm, 174 Hurley

Course Syllabus

On Stability

David Hoff, STABILITY AND CONVERGENCE OF FINITE DIFFERENCE METHODS FOR SYSTEMS OF NONLINEAR REACTION-DIFFUSION EQUATIONS, SIAM J. Numer. Anal. 15(6):1978
Eitan Tadmor, A REVIEW OF NUMERICAL METHODS FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, Bulletin of the AMS, 49(4):507-554, 2012

Introduction to Multigrid


W.L. Briggs, V.E. Henson and S.F. McCormick, A Multigrid Tutorial.

Reference Books for FEM

  • S. Brenner and L. Scott, The Mathematical Theory of Finite Element Methods
  • K. Eriksson, D. Estep, P. Hansbo, and C. Johnson, Computational Differential Equations, ISBN 0-521-56738-6
  • F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods
  • Unified Analysis of DG Methods for Elliptic Problems
  • An Analysis of Three Different Formulations of the Discontinuous Galerkin Method for Diffusion Equations
  • Considerations for 2D computer implementation

    References for numerical methods for conservation laws

    Chapters of "R.J. LeVeque, Numerical Methods for Conservation Laws"

    C.-W. Shu, ENO and WENO schemes for hyperbolic conservation laws

    SIAM Review Paper on History of Finite Element Method

    Sobolev Space

    Numerical Methods for Solving NS Equations

    Chorin, Numerical Solution of the NS Equations

    Brown etal, Accurate Porjection Methods for the Incompressible NS Equations

    Kuo etal, Two-Coler Fourier Analysis of Iterative Algs. for Elliptic Problems with Red/Black Ordering