Module: Numerics of Partial Differential Equations
|Numerics of Partial Differential Equations||Lecture||2||Winter Semester|
|Numerics of Partial Differential Equations||Recitation Section (small)||2||Winter Semester|
Prof. Sabine Le Borne
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
- 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
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.
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.
- 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:
Workload in Hours:
Independent Study Time: 124, Study Time in Lecture: 56
Course: Numerics of Partial Differential Equations
Sabine Le Borne, Patricio Farrell
German & English
Elementary Theory and Numerics of PDEs
- types of PDEs
- well posed problems
- finite differences
- finite elements
- finite volumes
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