News
April 12: The last lecture will be on April 15 at 10.15 in 2344.
February 10: The schedule for lectures has been changed to Tuesdays and Mondays, see below.
Mathematical and numerical techniques for PDE
This course is given at graduate level and corresponds to 10 hp. The goal is to give an overview of important numerical and mathematical concepts related to PDEs, but also to discuss in detail some techniques, such as analysis of boundary conditions in continuous and discrete settings, and how to use linearization to develop a non-linear theory. Some knowledge of function spaces and functional analysis is useful.
There will be 10 lectures, 4 sets of homework problems, and 1 research papers to read and present. The preliminary plan is to have lectures on Fridays 13-15, but if there is a strong wish for something else please let me know, and maybe a different schedule can be determined.
literature:
[1] Gustafsson, Kreiss, Oliger, Time dependent problems and difference methods, 2nd edition, Wiley 2013
[2] Kreiss, Lorenz, Initial-Boundary value problems and the Navier-Stokes Equations, SIAM 2004
[3] Evans,Partial Differential Equations, AMS
[4] Some FEM text, for example Grossmann,Roos,Stynes, Numerical Treatment of Partial Differential Equations (Ch 4.1-4.4)
For more on hyperbolic conservation laws see
[5] LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge 2002
teacher:
First lecture: February 8, 13.15-15, room 2344
outline of the course:
| date&time | room | topic | reading | problem set | |
|---|---|---|---|---|---|
| 1 | Feb 8, 13-15 | 2344 | Introduction and discussion of mathematical properties of different types of PDEs | Ch1 in [1] |
problem set 1 due Mar 1 |
| 2 | Feb 15, 13-15 | 1311 | Wellposedness and stability for time-dependent PDE | Ch3&4 in [1] | |
| 3 | Feb 19, 13-15 | 2345 | more about wellposedness and stability | Ch3 in [2] | |
| 4 | Feb 26, 13-15 | 2347 | elliptic PDEs | Evans Ch6 |
problem set 2 due Mar 22 |
| 5 | Mar 5, 13-15 | 2345 | more on elliptic | ||
| 6 | Mar 12, 13-15 | 2344 | Non-linear example | Ch4&5 in [2] | |
| 7 | Mar 19, 13-15 | 2344 | Non-linear example | Ch 7 in [1] |
problem set 3, due April 12 |
| 8 | Mar 25, 13-15 | 2344 | IBVP:energy method | Ch 8&11 in [1] | |
| 9 | April 8 13-15 | 2344 | IBVP:normal mode analysis | Ch 9&12 in [1] |
problem set4, due May 3 |
| 10 | April 15, 10-12 | 2344 | Discrete normal mode analysis | ||
| May 10, 9-15 | TBA | paper presentations and discussions | List of suggested papers |
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Paper presentations: May 10. I expect everyone to attend all presentations!