Department of Information Technology

Mathematical and numerical techniques for PDE

NEWS: Deadline for handing in remaining homework problems: February 20!

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.

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:

Gunilla Kreiss

First lecture: October 8, 10.15-12 in room 6102

outline of the course:

date&time room topic reading problem set
1 Oct 8, 10-12 6102 Introduction and discussion of mathematical properties of different types of PDEs Ch1 in [1] problem set 1 due October 27
2 Oct 17, 13-15 6102 Wellposedness and stability for time-dependent PDE Ch3&4 in [1]
3 Oct 22, 10-12 2344 more about wellposedness and stability Ch3 in [2]
4 Oct 29, 10-12 2344 elliptic PDEs Evans Ch6 problem set 2 due December 1
5 Nov 6, 10-12 2345 more on elliptic
6 Nov 19, 10-12 2345 Non-linear example Ch4&5 in [2]
7 Dec 10, 10-12 1111 Non-linear example Ch 7 in [1] problem set 3 due January 14
8 Dec 17, 10-12 2345 IBVP:energy method Ch 8&11 in [1]
9 Jan 14, 10-12 2345 IBVP:normal mode analysis Ch 9&12 in [1] problem set 4 due January 30
10 Jan21, 10-12 2345 error estimates
Jan 30, 10-12, 13-16 paper presentations and discussions List of suggested papers

Paper presentations: January 30. I expect everyone to attend all presentations.

Updated  2015-09-28 16:47:12 by Anneli Folkesson.