Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-37-M-7

High-Order Methods for Hyperbolic Equations (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-37-M-7 High-Order Methods for Hyperbolic Equations 4.5 CP (135 h)


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-37-K-7
High-Order Methods for Hyperbolic Equations
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-37-K-7]: Title: "High-Order Methods for Hyperbolic Equations"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86249 ("High-Order Methods for Hyperbolic Equations")

Evaluation of grades

The grade of the module examination is also the module grade.


The mathematical concepts for the numerical treatment of systems of hyperbolic conservation equations with high order of approximation in place and time are described and investigated. In particular, the following contents are discussed:
  • discontinuous Galerkin method,
  • ADER method (incl. WENO reconstruction),
  • strong stability preserving (SSP) time stepping.

Competencies / intended learning achievements

Upon sucxcessful completion of this module, the students have mastered the theory of various high-order methods used for solving systems of hyperbolic conservation laws. They are able to analyze the algorithms and to apply them to specific problems. In addition, they are able to critically assess the applicability and limitations of the algorithms. They understand the proofs presented in the lecture and are able to comprehend and explain them. Inparticular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements.

Working on concrete tasks, they have gained aprecise and independent handling of terms, propositions and methods of the lecture.


  • J. S. Hesthaven, T. Warburton: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications,
  • B. Cockburn: An Introduction to the Discontinuous Galerkin Method for Convection-Dominated Problems,
  • E. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics,
  • S. Gottlieb: On High Order Strong Stability Preserving Runge–Kutta and Multi Step Time Discretizations.

Requirements for attendance of the module (informal)

Knowledge from the module [MAT-81-12-M-7] is desirable.


Requirements for attendance of the module (formal)


References to Module / Module Number [MAT-81-37-M-7]

Module-Pool Name
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)