Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-12-M-7

Numerical Methods for Hyperbolic PDE (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-12-M-7 Numerical Methods for Hyperbolic PDE 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in WiSe
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V MAT-81-12-K-7
Numerical Methods for PDE II
P 56 h 214 h - - PL1 9.0 WiSe
  • About [MAT-81-12-K-7]: Title: "Numerical Methods for PDE II"; Presence-Time: 56 h; Self-Study: 214 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86341 ("Numerical Methods for Hyperbolic PDE")

Evaluation of grades

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


Contents

Numerical methods which deal with hyperbolic differential equations will be discussed and analytically analyzed. In particular, the following topics are covered:
  • approximation methods for hyperbolic problems,
  • theory of weak solutions and entropy solutions,
  • consistency, stability and convergence,
  • (if possible) approximation methods for systems of conservation equations.

Competencies / intended learning achievements

Upon successful completion of this module, the students have studied and understand the basic concepts for the numerical treatment of hyperbolic differential equations as well as mathematical techniques required to analyze these methods. They understand the mathematical background required for the methods used and they are able to critically assess the possibilities and limitations of the use of these methods. They are able to name and to prove the essential statements of the lecture as well as to classify and to explain the connections. In particular, they are able to outline the conditions and assumptions that are necessary for the validity of the statements.

By completing given tasks and exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture.

Literature

  • E.F. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics,
  • R. LeVeque: Finite Volume Methods for Hyperbolic Problems,
  • E. Godlewski, P.-A. Raviart: Numerical Approximations of Hyperbolic Systems of Conservation Laws.

References to Module / Module Number [MAT-81-12-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.)