Advanced Finite Elements
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
MA5337 is a semester module in English language at Master’s level which is offered every semester.
This Module is included in the following catalogues within the study programs in physics.
- Catalogue of non-physics elective courses
|Total workload||Contact hours||Credits (ECTS)|
|210 h||75 h||7 CP|
Content, Learning Outcome and Preconditions
- Mixed and Hybrid Finite Elements
- Discontinuous Galerkin Methods
- Nonconforming Methods
- Adaptive Finite Element Method
- Isogeometric analysis
- Reduced Basis
- Treatment of nonlinear PDEs
- Modern Iterative Solvers and Preconditioning
- Applications in Solid Mechanics and Incompressible Fluid Mechanics
Helpful but not necessary: Functional Analysis (MA3001)
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|VO||2||Advanced Finite Elements [MA5337]||
Tue, 12:00–14:00, MI 03.10.011
|UE||2||Advanced Finite Elements (Exercise Session) [MA5337]||
Tue, 14:00–16:00, MI 03.10.011
|UE||1||Advanced Finite Elements (Central Exercise Session) [MA5337]||
Thu, 08:30–10:00, MI 02.04.011
|UE||2||Advanced Finite Elements (Programming Tutorial) [MA5337]||
Thu, 10:00–14:00, MI 02.04.011
Learning and Teaching Methods
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.
Mathematical Aspects of Discontinuous Galerkin Methods.
Mathematics and Applications 69, Springer, Heidelberg, 2012.
Alexandre Ern and Jean-Luc Guermond:
Theory and practice of finite elements.
Applied Mathematical Sciences 159, Springer, New York, 2004.
Alfio Quarteroni and Alberto Valli:
Numerical approximation of partial differential equations.
Springer Series in Computational Mathematics 23, Springer, Berlin, 1994.
J. Austin Cottrell; Thomas J.R. Hughes; Yuri Bazilevs
Isogeometric Analysis: Toward Integration of CAD and FEA
D. Boffi, F. Brezzi, M. Fortin
Mixed Finite Element Methods and Applications
Hesthaven, Rozza, Stamm
Certified Reduced Basis Methods for Parametrized Partial Differential Equations
Alfio Quarteroni, Andrea Manzoni, Federico Negri
Reduced Basis Methods for Partial Differential Equations
Description of exams and course work
The exam may be repeated at the end of the semester.