Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-11-M-7

Numerical Methods for Elliptic and Parabolic PDE (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-11-M-7 Numerical Methods for Elliptic and Parabolic PDE 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in SuSe
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+2U MAT-81-11-K-7
Numerical Methods for PDE I
P 84 h 186 h - - PL1 9.0 SuSe
  • About [MAT-81-11-K-7]: Title: "Numerical Methods for PDE I"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86340 ("Numerical Methods for Elliptic and Parabolic PDE")

Evaluation of grades

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


Contents

Continuation of the courses [MAT-80-11A-K-4] and [MAT-80-11B-K-4]. Numerical methods that deal with elliptic and parabolic differential equations will be discussed and analytically analyzed. In particular, the following topics will be covered:
  • approximation methods for elliptic problems,
  • theory of weak solutions,
  • consistency, stability and convergence,
  • approximation methods for parabolic problems.

Competencies / intended learning achievements

Upon completion of this module, the students have studied and understand basic concepts to deal with numerical aspects of partial differential equations as well as mathematical techniques to analyze these methods. They understand the mathematical background required for the methods used and they can 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 the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.

Literature

  • D. Braess: Finite Elemente,
  • A. Quarteroni, A. Valli: Numerical Approximation of PDEs,
  • C. Grossmann, H.-G. Roos: Numerische Behandlung partieller Differentialgleichungen.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

References to Module / Module Number [MAT-81-11-M-7]

Course of Study Section Choice/Obligation
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics Statistics and Computational Methods [WP] Compulsory Elective
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.)