Target Audience:
The lab exercises are dedicated to participants of the lecture Numerical Analysis and Simulation II: PDEs. For general information on lab exercises corresponding to the Master programme Mathematics, see the handbook (page 115).

Contents:
The lab exercises include the implementation of methods, which are introduced in the lecture Numerical Analysis and Simulation II: PDEs. The methods are implemented using the software package OCTAVE or MATLAB . Four lab exercises will be provided corresponding to the topics:

• elliptic PDEs (of second order)
• parabolic PDEs (of second order)
• hyperbolic PDEs of second order
• hyperbolic PDEs of first order (conservation laws)

Procedure:
There will be four lab exercises in the period April - July 2012. The 3 credit points of this course are achieved if three of the four lab exercises are implemented successfully. The exercises can be done in groups of 1-3 persons. Each group will present and explain their implementations at corresponding meetings. A list of possible dates will be provided for each lab exercise. There will not be a weekly meeting for all participants. Nevertheless, a weekly office hour will be provided, where questions can be discussed.

Literature:

• D.  Braess, Finite Elements, (3rd ed.) Cambridge University Press, 2007.
• W.L. Briggs, A Multigrid Tutorial, SIAM, 1987.
• Ch. Großmann, H.-G.  Roos, M.  Stynes, Numerical Treatment of Partial Differential Equations, Springer, 2007. (parts of Chapters 1-4)
• W. Hackbusch, Elliptic Differential Equations: Theory and Numerical Treatment, Springer, 1992.
• P. Knabner, L. Angermann, Numerical Methods for Elliptic and Parabolic Partial Differential Equations, Springer, 2003.
• R.J.  LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, Basel, 1992.
• H.R.  Schwarz, J.  Waldvogel, Numerical Analysis, A Comprehensive Introduction, John Wiley & Sons, 1989. (Chapter 10)
• J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Chapman & Hall, 1989.