Numerical Analysis and Simulation II: Partial Differential Equations (PDEs)

Summer Term 2015

Organizers

Prof. Dr. M. Günther

Dr. C. Heuer

J. Silva M. Sc.

Type

Lecture and Exercises (4+2 SWS)
The course comprises 4h lectures and 2h exercises per week.
Lab exercises are part of a separate course.

Target audience

The course is dedicated to students in mathematics, financial mathematics, computer simulation in science, IT and SII.

Prerequisite

Knowledge of basic courses in mathematics (Analysis I-II, Linear Algebra I-II or similar), Introduction to Numerical Mathematics (or: block course 'Introduction to Numerical Methods for Computer Simulation') and Numerical Analysis and Simulation I: ODEs.

Credits

9 Credit Points

Lab Exercise

Separate course: Lab Exercises for Numerical Analysis and Simulation II: PDEs

Examination

There will be a written examination at the end of the term.

Topics

Numerical methods for partial differential equations.

Time and Place

Lecture:
Tuesdays, Thursdays 14:00-16:00

Exercises:

Tuesdays 16:00-18:00

Script

• A. Arnold, M. Ehrhardt, S. Rjasanow, Numerik partieller Differentialgleichungen, 2005.
• R. Pulch, Numerical Analysis and Simulation of Partial Differential Equations, Lecture Notes, 2011.

Exercises

• Question Sheet 1

• Question Sheet 2

• Question Sheet 3

• Question Sheet 4

• Question Sheet 5

• Question Sheet 6

• Question Sheet 7

• Question Sheet 8

• Question Sheet 9

• Question Sheet 10

• Question Sheet 11

• Solutions Homework

• Solutions Exercises

• Solutions Exercises 10

Literature

• D. Braess, Finite Elemente, Springer, 1997.
• W.L. Briggs, A Multigrid Tutorial, SIAM, 1987.
• A. Borzi, Introduction to Multigrid Methods, University of Würzburg.
• M.J. Gander, G. Wanner, From Euler, Ritz and Galerkin to Modern Computing , erscheint in SIAM Review, 2012. (Folien), Hard to find historical references
• C. Grossmann, H.-G. Roos, Numerik Partieller Differentialgleichungen, Teubner, 1994.
• G. Haase, U. Langer, Multigrid Methods: From Geometrical to Algebraic Versions, 2001.
• W. Hackbusch, Theorie und Numerik elliptischer Differentialgleichungen, Teubner, 1996
• W. Hackbusch, Integralgleichungen,Theorie und Numerik, Teubner, 1997.
• P. Knabner und L. Angermann, Numerik partieller Differentialgleichungen, Springer, 2000.
• S. Larsson, V. Thomee, Partial Differential Equations with Numerical Methods, Springer, 2005.
• A.M. Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations , Springer, 2008.
• M. Renardy, R.C. Rogers, An Introduction to Partial Differential Equations, Springer, 2004.
• J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Chapman & Hall, 1989.