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Advanced Finite Element Methods

Module MA4303

This Module is offered by TUM Department of Mathematics.

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.

Module version of WS 2012/3

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2013WS 2012/3

Basic Information

MA4303 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 workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Advanced finite element techniques such as, e.g.,
- Mixed and Hybrid Finite Elements
- Discontinuous Galerkin Methods
- Nonconforming Methods
- Adaptive Finite Element Method
- Isogeometric analysis
- Modern Iterative Solvers and Preconditioning
- Applications in Solid Mechanics and Incompressible Fluid Mechanics

Learning Outcome

The main goal of this module is to deepen the understanding of the derivation and analysis of advanced finite element techniques and suitable efficient solvers. The discussion is accompanied by relevant examples from solid and fluid mechanics, which enables students to develop some initial competence for choosing appropriate discretization techniques for different physical problems. At the end of this module, students are able to engage in current research topics and to study advanced finite element literature independently.


MA2304 Numerical Methods for Ordinary Differential Equations, MA3303 Numerical Methods of Partial Differential Equations
The theory and implementation of conforming finite elements for elliptic second order PDEs is supposed to be known.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

lectures, tutorials, project teams
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.


blackboard, slides, assignment sheets, lab exercises


- Daniele Antonio Di Pietro and Alexandre Ern:
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.

Module Exam

Description of exams and course work

The examination consists of a written exam (60 minutes). Students have to understand advanced finite element techniques and can choose appropriate discretization techniques. They are able to apply them to relevant examples from solid and fluid mechanics in limited time.

Exam Repetition

The exam may be repeated at the end of the semester.

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