Adaptive finite elements (spring 2015)

Organization

The final grade will be based on assignments (2/3) (lowest two grades will be ignored) and a computer exercise (1/3).

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 2: Classification of second order PDEs into elliptic, parabolic and hyperbolic ones. Model examples: Poisson, heat and wave equation. Book: Sect. 0.1-4
• February 9: Sect 1.1-5
• February 16: Sect. 1.6-7. Sect. 2.1-5
• February 23: Sect. 2.6-9. Sect. 3.1
• March 2: Sect. 3.2-3
• March 9: Sect. 3.4-5. Additional notes: Thm 1.1 (Bramble-Hilbert)
• March 16: Additional notes: Sect. 1-3
• March 23: Sect. 5.1-5
• March 30: Additional notes: Sect. 7-8
• April 13: Additional notes: Sect. 9-11
• April 20: Additional notes: Proof of Thm. 11.4

Exercises

• February 2: 0.x: 2, 3, 8. Extra 1
• February 9: 0.x: 6. 1.x: 1, 3, 4 (do it for n=2,3 only), 5
• February 16: 1.x: 8, 13, 10, 16
• February 23: 1.x: 20, 35. extra 18. 2.x: 9, 11
• March 2: 3.x: 14 (only for linears), 17, 18, 19 (ok to do it for k=1,2,3), 30
• March 9: 3.x: 27, 6, 9, 15. Extra: 3
• March 16: extra 4, 7, 11 (use Thm. 1.6.6). 5.x.2
• March 23: 5.x.1. extra: 5, 6, 12.
• March 30: 9.x.5 (replace hint by: Use equivalence of norms on finite dimensional spaces), 9.x.7, extra 15
• April 13: extra 14, 16, 17