MTH 655
and
MTH 659 (Numerical Analysis)
Numerical Functional Analysis with Applications
- Winter 2011
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| Assignments |
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- Assignment 1: read all the problems, solve only those indicated
or more for extra credit. Due Wed. 1/12.
Group B: choose three out of 1.3.11, 7.1.3, 7.1.4, 7.2.3
Group A: 7.1.5, 7.3.12 or 7.3.14 (read 7.3.11 for both), read 7.4 and solve 7.4.1
- Assignment 2 (due 1/24): use fem1d.m or your own code. Consider
(i) a smooth solution $u$ of your choice, and (ii) u(x)=x-x^{alpha}
where alpha=4/3 or 2/3.
Group B: show convergence in H_0^1 and L^2 norms for (i). Discuss
the BVP with (ii) and any issues you see with its (FE) implementation.
Group A: discuss available theory for (FE) solution for (ii) (can you
verify it ?) Try different norms.
- Assignment 3 (due 2/14): problems #1-#5 from the worksheet distributed in class on
interpolation and quasi-interpolation.
All: #1 or #2, #4B/A as indicated. #5 is a challenge problem (extra credit).
Group B: 3.3.8, 3.4.1, #3
Group A: 3.3.8, 3.4.2, #3 or #5
- Assignment 4 (due midnight, 3/16, in my
mailbox): assignment . Group B: 1,2, and
(3 or 4). Group A: 1, 3, 4. (Note from 3/3/11: correction was made to
constants in problem 4).
Extra credit A): use ACF code (continuous Galerkin FE) as explained in
class in dead week.
ACF (Alberty/Carstensen/Funken)
code available from "Software", "Short finite element implementation"
Extra credit B): use BC (mixed method) as explained in class in dead week.
BC (Bahriawati/Carstensen)
code available from "Software", "Mixed finite element implementation" .
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