Math 269C, Section 1, Spring 2006
Advanced Numerical Analysis
Lecture Meeting Time: MWF 2.00PM - 2:50PM.
Lecture Location: MS 5118.
Instructor: Luminita A. Vese
Office: MS 7620D
Office hours: M 3-4, W 3-4, F 4-5, (schedule subject to change), or by appointment.
(placed on reserve for 2 hours/overnight at SEL Library).
Claes Johnson, Numerical solution of partial differential equations by
the finite element method, Cambridge University Press, 1987.
O. Axelsson and V. A. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation, Academic Press, London, 1984.
Braess, D. Finite elements. Theory, fast solvers, and applications in solid mechanics.
Translated from the 1992 German original by Larry L. Schumaker. Cambridge University Press, Cambridge, 1997.
S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, 1996.
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, Vol 15, Springer-Verlag, New York, 1991.
Ciarlet, P.G. The finite element method for elliptic problems.
Studies in Mathematics and its Applications, Vol. 4. North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978.
P. G. Ciarlet and J. L. Lions, Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part I), North-Holland, 1991.
Girault, V., Raviart, P.-A. Finite element methods for Navier-Stokes equations. Theory and algorithms.
Springer Series in Computational Mathematics, 5. Springer-Verlag, Berlin-New York, 1986.
Girault, V., Raviart, P.-A. Finite element approximation of the Navier-Stokes equations. Springer-Verlag, Berlin-New York, 1981.
T. J. R. Hughes, The Finite Element Method, Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1987, Dover, 2000.
A. R. Mitchell and R. Wait, The Finite Element Method in Partial Differential Equations, John Wiley & Sons, Ltd, 1977.
Pironneau, O. Finite element methods for fluids.
Wiley, New York; Masson, Paris, 1989.
H. R. Schwarz, Finite Element Methods, in Computational Mathematics and Applications, Academic Press, 1988.
W. G. Strang and G. J. Fix, An Analysis of the Finite Element Method, Wellesley Cambridge Press, 1973.
B. Szabo and I. Babuska, Finite Element Analysis, John Wiley & Sons, 1991.
R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, 3rd ed., North-Holland, 1984.
V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Springer Series in Computational Mathematics, Vol. 25, Springer Verlag, 1997.
O. C. Zienkiewicz, The Finite Element Method, 3rd ed, McGraw-Hill, New York, 1977.
O. C. Zienkiewicz and K. Morgan, Finite Elements and Approximation, John Wiley & Sons, 1983.
O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method: Volume 1, The Basis, Butterworth-Heinemann, 2001.
O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method: Volume 2, Solid Mechanics, Butterworth-Heinemann, 2001.
O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Volume 3, Fluid Mechanics, Butterworth-Heinemann, 2001.
J. Tinsley Oden, Graham F. Carey, The Texas Finite Element Series,
Finite Elelemnts, Vols: I-VI, Prentice Hall.
Pre-requisites: Math 115A, 135A, 151A, 151B.
Virtual Office Hours
PIC Lab: Boelter Hall 2817 and
Mathematical Sciences 3970
MATLAB Documentation (thanks to Prof. C. Anderson, UCLA)
Class Web Page: http://www.math.ucla.edu/~lvese/269c.1.06s/
Numerical Analysis Qualifying Exam
Getting started with MATLAB
There will be several homework assignments on theoretical questions, and two
The final exam will be on the last day of the class (June 9).
HW 30%, Projects 20%, Midterm 20%, Final 30%
Homework Assignments, Projects & Practice Problems:
HW #1 (due on Monday, April 17)
HW #2 (due on Friday, April 28)
Computational Project 1 (due on Friday, May 19)
HW #3 (due on Friday, May 12)
Computational Project 2 (due on Friday, June 9)
HW #4 (due on Friday, May 26)
HW #5 (due on Friday, June 9)
ADDITIONAL NOTES AND PRACTICE PROBLEMS
Two problems with partial solutions