Institute for Numerical Simulation
Rheinische Friedrich-Wilhelms-Universität Bonn

Lecture in WS 2014/15:

Numerical Algorithms (V4E1)

Prof. Dr. Sven Beuchler

Assistant: Katharina Hofer

The topics of the lecture are hp-Finite Element Methods, theory and numerics of conservation laws and the Discontinous Galerkin Method.

Compulsory prior knowledge

Wissenschaftliches Rechnen I / Scientific Computing I

Lecture and Tutorial

The lecture will be Tuesdays from 10:15 - 12:00 and alternating with the tutorial Thursdays from 8:30 - 10:00 or Wednesdays from 16:00 - 17:30. (On October, 15, the lecture starts at 16:15) The lecture and the tutorial will be in held in the Wegelerstraße 6, Seminarraum 6.020.

week Tuesday Wednesday Thursday
06.10-10.10 Lecture - Lecture
13.10-17.10 Lecture Lecture Lecture
20.10-24.10 Lecture Lecture Tutorial
27.10-31.10 Lecture Tutorial Lecture
03.11-07.11 Lecture Tutorial -
10.11-14.11 Lecture Lecture Tutorial
17.11-21.11 Lecture Tutorial Lecture
24.11-28.11 Lecture Lecture Tutorial
01.12-05.12 Lecture - Lecture
08.12-12.12 Lecture Lecture Tutorial
15.12-19.12 Lecture Tutorial Lecture
22.12-26.12 - - -
05.01-09.01 Lecture Lecture Lecture
12.01-16.01 Lecture Tutorial Tutorial
19.01-23.01 Lecture Tutorial Lecture
26.01-30.01 Lecture - -

Consultation hour of Prof. Beuchler: Wednesdays 10:30-11:30.

Final Exam

The oral examinations will take place on the 4th/6th of February and the 25th of March 2015!

Lecture Script

The current version (11.12.2014) of the lecture script can be found here: LectureScript.


For admittance to the final exam you have to score 50% or more points for both, the theoretical and the programming exercises, separately. If you want to use the prepared code for the programming exercises please send an e-mail to .
  1. sheet1.pdf
  2. sheet2.pdf
  3. sheet3.pdf
  4. sheet4.pdf
  5. sheet5.pdf
  6. sheet6.pdf
  7. (corrected on 13.11.2014)
  8. sheet7.pdf
  9. sheet8.pdf
  10. (corrected closing date)
  11. sheet9.pdf
  12. sheet10.pdf
  13. sheet11.pdf
  14. sheet12.pdf


  • Ch. Schwab: p-and hp-Finite Element Methods. Oxford University Press, 1998
  • L. Demkowicz: Computing with hp-adaptive Finite Elements, Chapman and Hall
  • G. Karniadakis, S.Sherwin: Spectral/hp Element Methods for Computational Fluid Dynamics, Oxford Science Publications, 2005
  • D. Di Pietro, A. Ern: Mathematical Aspects of Discontinuous Galerkin Methods, Springer, 2012
  • J. Hesthaven, T. Warburton: Nodal Discontinuous Galerkin Methods. Algorithms, Analysis and Applications. Springer, 2008
  • R. Leveque: Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics, 2002
  • D. Kroener: Numerical Schemes for Conservation Laws. Wiley, Teubner, 1997
  • B. Cockburn: Discontinuous Galerkin methods. Plenary lecture presented at the 80th Annual GAMM Conference, Augsburg, 25-28 March 2002
  • Programming