Numerical Methods for stationary PDEs (spring 2016)
Organization
Time and venue: Utrecht University, 10:00 - 12:45 hrs, Buys Ballot Building (BBG).
Usually, lectures during 2 * 45 min + 45 min exercise class.
The final grade will be based on assignments (40%) (lowest grade will be ignored), a
computer exercise (25%), and an exam (35%, minimal grade 4)
Literature:
Primary:
Brenner, Susanne C.; Scott, L. Ridgway The mathematical theory of finite element methods. Third edition. Texts in Applied Mathematics, 15. Springer, New York, 2008. xviii+397 pp. ISBN: 978-0-387-75933-3, The book.
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
Ricardo H. Nochetto and Andreas Veeser.
Primer of Adaptive Finite Element Methods
Additional notes
Lectures
- February 17(BBG 315/317): Classification of second order PDEs into elliptic, parabolic and hyperbolic ones. Model examples: Poisson, heat and wave equation. Book: Sect. 0.1-4
- February 24 (BBG 315/317): Sect. 0.5-6, Sect. 1.1-3 until Thm. 1.3.4
- March 2 (BBG 315/317): rest Ch. 1, Sect 2.1-3
- March 9 (BBG 079): Sect 2.4-7
- March 16 (BBG 315/317): Sect. 2.8-9, Sect. 3.1-2 until (3.2.3)
- March 23 (BBG 079): Sect 3.2-3
- March 30 (BBG 315/317): Sect. 3.4
- April 6 (BBG 201): Sect. 3.5, Bramble-Hilbert lemma
- April 13 (BBG 201): Sect. 1-3 of Additional Notes.
- April 20 (BBG 201): Sect. 5.1-3.
- May 4 (BBG 169): Sect. 5.4-5. Sect. 4.8. Sect. 4-6 of Additional Notes
- May 11 (BBG 169): Thm 7.1, Sect. 8 of Additional Notes.
- May 18 (BBG 169):
- May 25 (BBG 169):
- June 1: exam
- June 22: retake (or near this date after consultation)
Extra exercises
Exercises
- February 17: 0.x: 2, 3, 8. Extra 1
- February 24: 0.x: 6. 1.x: 1, 3, 4 (suffices to do it for n=2,3 only)
- March 2: 1.x.5, 1.x.8, 1.x.13, 1.x.35
- March 9: 1.x.10, 1.x.16, 1.x.20, extra 18
- March 16: 2.x.9, 2.x.11, 3.x.14 (only for linears), 3.x.17
- March 23: extra 2, 3.x: 18, 19 (ok to do it for k=1,2,3), 30, 27 (construct an example where the element is not C^1) (please hand them in before Tuesday 29-3, 17:00)
- March 30: 3.x: 28 (of course with proof), 6, 9, 13, 15. Please have the ``Additional notes'' available next week.
- April 6: extra 3 (hint: Bramble-Hilbert), 5.x.1, 5.x.2
- April 13: extra 4, 7, 11
- April 20: extra 5, 6, 12
- May 4: exercises -1, 0 from `Additional notes', 9.x.5, 9.x.7 (replace hints by: Use equivalence of norms on finite dimensional spaces)
- May 11: extra 14, 15
- May 18: extra 16, 17
- May 25: