Numerical Methods for stationary PDEs (spring 2010)
Organization
Time and venue: Wednesdays 10:15 - 13:00 hrs in weeks 5-11 and 13-20, Vrije Universiteit, W&N Building. Usually, lectures during 2 * 45 min + 45 min exercise class.
The final grade will be based on assignments (75%) and a
computer exercise (25%). This exercise should be handed in on June 23.
Literature:
primary (we will do 5 chapters from this book):
Brenner, Susanne C.; Scott, L. Ridgway.
The mathematical theory of finite element methods.
Second edition. Texts in Applied Mathematics, 15. Springer-Verlag, New York, 2002. xvi+361 pp. ISBN: 0-387-95451-1 (or the third edition from 2008) , the book
Additional notes
Additional exercises
secondary:
Braess, Dietrich.
Finite elements. Theory, fast solvers, and applications in elasticity theory. Translated from the German by Larry L. Schumaker. Third edition. Cambridge University Press, Cambridge, 2007. xviii+365 pp. ISBN: 978-0-521-70518-9
Ciarlet, Philippe G.
The finite element method for elliptic problems.
North-Holland, Amsterdam,1978
Johnson, Claes.
Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Cambridge, 1987. 278 pp. ISBN: 0-521-34514-6;
Lectures
- February 10 (room M639): Classification of second order PDEs into elliptic, parabolic and hyperbolic. Book: pp 1-8 without 6
- February 17 (M639): Sect. 0.1-0.6, 1.1-1.4
- February 24 (M639): Remainder of Sect. 1
- March 3 (M639): Sect 2.1 - 2.5
- March 10 (M639): rest of Ch.2., p 69-70.
- March 17 (M639): Ch. 3 until (3.3.9) on page 79
- March 24 (M143): until (3.4.6) on p83.
- March 31 (M639): rest of Chapter 3. Bramble-Hilbert lemma from the additional notes.
- April 7 (M639): p1-3 from additional notes.
- April 14 (M639): Sect. 5.1, 5.2, 5.3.
- April 21 (M639): Sect. 5.4, 5.5, 5.6 (partly). Sect. 5 from notes.
- April 28 (M639): Notes: Sect 6, 7.1, 7.2
- May 5: no lecture
- May 12 (M639): Notes: Sect 7.4, 7.5
- May 19 (M639): Notes: Sect. 8, 9
- May 26: no lecture
Exercises
- February 10: prove that set of "hat" functions is a basis, and give matrix vector formulation of Ritz-Galerkin approximation.
- February 17: 0: 2, 4. 1: 1, 3, 4, 5, 10.
- February 24: 1: 8, 13, 16, 20, 21, 35
- March 3: 1: 37. 2: 1, 2, 3, 4, 10, 11 + Show that for any k, the differential equation from 2.x.10, but with boundary conditions u(0)=u(1)=0, leads to a coercive bilinear form over the ``energy space'' V.
- March 10: 2: 7, 8, 9. 3: 10, 30.
- March 17: Additional exercise 1, 3: 1, 17, 18, 19
- March 24: 3: 6, 13, 14, 27, 28
- March 31: 3: 8, 9, 15, additional exercise 2
- April 7: additional exercise 3. Using the transformation lemma, prove Thm 4.1 of ``additional notes''. Ch. 5: 1, 2.
- April 14: 5.x.13, additional exercises 4, 5.
- April 21: additional excercises 6, 8. Exercises -1, 0 from notes
- April 28: Notes: exer. 1-4 from notes
- May 5: no class
- May 12: exer. 5, 8, 9, 10, 11, 12, 13 from notes
- May 19: exer. 14-18. Hand in on June 2.