Math 269C, Section 1, Spring 2020
Advanced Numerical Analysis: The Finite Element Method
Lecture Meeting Time: Monday 1-1.50pm AND Friday 1-2:50pm. (please note special lecture time)
Lecture Location: Online via Zoom (information will be sent by email before the lecture).
Instructor: Luminita A. Vese
Office: MS 7620D
Office hours: Virtual office hours.
(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 (or the 2nd edition, 2009).
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.
H. Attouch, G. Buttazzo, and G. Michaille, Variational Analysis in Sobolev and BV Spaces: applications to PDE's and optimization, MPS-SIAM 2006.
Enforced Requisites: courses 115A, 151A, 151B.
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.1.19s/
Numerical Analysis Qualifying Exam
Getting started with MATLAB
There will be several homework assignments on theoretical questions, and two
Homework 75%; Projects 25%.
Homework Assignments, Projects & Practice Problems:
HW #1 (due on Monday, April 20)
HW #2 (due on: Monday, April 27)
Computational Project 1 (due on: Monday, May 18)
HW #3 (due on: Friday, May 15)
Computational Project 2 (due on Friday, June 5)
Project 2 (pdf)
Project 2 (LaTex)
HW #4 (due on Friday, May 29)
HW #5 (due on June 12)
ADDITIONAL NOTES AND PRACTICE PROBLEMS
Two problems with partial solutions