Syllabus

MACS/MAGN 550
Numerical Analysis of Partial Differential Equations
Spring 1994, 134 Alderson Hall 11:00-12:15 TTh

Instructor: Erik Van Vleck
Office: Stratton 216
Office Hours: TTh 1:30-2:30
Text: Hall and Porsching, Numerical Analysis of Partial Differential Equations

Outline:
Introduction to finite differences and finite elements
First-Order hyperbolic problems
Parabolic diffusion problems
Lax-Richtmyer theory
Sobolev spaces and approximation of functions
Elliptic problems
Special Topic 1: Iterative methods and preconditioning for linear systems
Special Topic 2: Adaptive meshing techniques

Grades:
Various Individual and Group Assignments (35)
2 Midterm Exams (50)
1 Final Individual Project (15)

Important Dates:
Midterm 1 (in class) on Thursday, February 17, 1994
Midterm 2 (in class) on Thursday, March 31, 1994
Final Project due Friday, April 29, 1994

All assignments due at the beginning of class
NO LATE ASSIGNMENTS ACCEPTED UNDER ANY CIRCUMSTANCES

Supplementary material:
Schaum's Outline: Partial Differential Equations.
C. Johnson, ``Numerical solution of the partial differential equations
by the finite element method,'' Cambridge (1987).
W. Strang and G. Fix, ``An Analysis of the Finite Element Method,''
Prentice-Hall (1973).
W. Ames, ``Numerical methods for partial
differential equations,'' Academic Press (1992).
G. Sod, ``Numerical methods in Fluid Dynamics,'' Cambridge (1985).
R. Richtmyer and K.W. Morton, ``Difference Methods for Initial
Value Problems,'' Wiley-Interscience (1967).
G. Forsythe and W. Wasow, ``Finite-difference methods for partial
differential equations,'' John Wiley (1960).
A. Mitchell and D. Griffiths, ``The finite difference method in partial
differential equations,'' Wiley (1980).
D. Gottlieb and S. Orszag, ``Numerical Analysis of Spectral Methods,''
SIAM (1977).
C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, ``Spectral Methods
in Fluid Dynamics,'' Springer-Verlag (1988).
Various papers on iterative methods and preconditioning techniques.
Various papers on adaptive meshing strategies.