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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.


MA2302 Introduction to Numerics, MA3301 Numerics of 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


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

written exam

Exam Repetition

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

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