Module Description

Module: Numerics of Partial Differential Equations

Courses:

TitleTypeHrs/WeekPeriod
Numerics of Partial Differential EquationsLecture2Winter Semester
Numerics of Partial Differential EquationsRecitation Section (small)2Winter Semester

Module Responsibility:

Prof. Sabine Le Borne

Admission Requirements:

None

Recommended Previous Knowledge:

  • Mathematik I - IV (for Engineering Students) or Analysis & Linear Algebra I + II for Technomathematicians
  • Numerical mathematics 1
  • Numerical treatment of ordinary differential equations

Educational Objectives:

Professional Competence

Theoretical Knowledge
  • Students can classify partial differential equations according to the three basic types.
  • For each type, students know suitable numerical approaches.
  • Students know the theoretical convergence results for these approaches.
Capabilities

Students are capable to formulate solution strategies for given problems involving partial differential equations, to comment on theoretical properties concerning convergence and to implement and test these methods in practice.

Personal Competence

Social Competence

Students are able to work together in heterogeneously composed teams (i.e., teams from different study programs and background knowledge) and to explain theoretical foundations.

Autonomy
  • Students are capable of checking their understanding of complex concepts on their own. They can specify open questions precisely and know where to get help in solving them.
  • Students have developed sufficient persistence to be able to work for longer periods in a goal-oriented manner on hard problems.

ECTS-Credit Points Module:

6 ECTS

Examination:

Oral exam

Workload in Hours:

Independent Study Time: 124, Study Time in Lecture: 56


Course: Numerics of Partial Differential Equations

Lecturers:

Sabine Le Borne, Patricio Farrell

Language:

German & English

Period:

Winter Semester

Content:

Elementary Theory and Numerics of PDEs

  • types of PDEs
  • well posed problems
  • finite differences
  • finite elements
  • finite volumes
  • applications

Literature:

Dietrich Braess: Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Berlin u.a., Springer 2007

Susanne Brenner, Ridgway Scott: The Mathematical Theory of Finite Element Methods, Springer, 2008

Peter Deuflhard, Martin Weiser: Numerische Mathematik 3

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