After successful completion of the course, students are able to...

• ... state and describe the components of modeling and numerical analysis, and analyze and categorize model equations with respect to their properties.
• ... explain the concept of a vector space and related topics such as scalar product, norm, basis, or discrete subspaces and give relevant examples.
• ... define and use the concept of the weak derivative.

• ... determine and analyze a corresponding weak form for a given partial differential equation, name types of boundary conditions, and evaluate and use given boundary conditions.
• ... describe and analyze aspects of polynomial interpolation relevant to the FEM.

• ... explain and apply the Galerkin FEM using the isoparametric principle, i.e. formulate expressions for the geometric representation of the computational domain or for the searched function using interpolation polynomials.
• ... calculate integrals from the FEM, if necessary by means of numerical integration, and select suitable methods as well as state, explain, and apply the concept of the reference element and examples thereof.
• ... illustrate and carry out the assembly process and evaluate properties of the system of linear equations produced in the FEM.

• ... explain the application of FEM to problems in structural or fluid mechanics and state their associated properties.
• ... state and illustrate the properties and procedures of the computational grids used in FEM.
• ... discuss and evaluate aspects of the (error) analysis of numerical methods.
• ... classify and apply time discretization methods.
• ... distinguish the collocation method from Galerkin-FEM.

The participants will be guided towards independently discretizing and solving a given partial differential equation. In particular, topics such as choice of basis functions, boundary conditions, and solution methods are essential to the course. The mathematical foundation is touched upon. The lecture is oriented towards partial differential equations relevant in engineering (e.g., solid mechanics or fluid mechanics). Common mistakes when using numerical methods are discussed.

Online lecture with power point presentation, derivation of equations, explaining sketches and figures; discussion of case studies

This course will be delivered in German language!

All exams are in German language only. Thus, please refer to the information in the German version of this page.

K.-J. Bathe: Finite Elemente Methoden, Springer Verlag, 1986;

Zienkiewicz, Taylor: The Finite Element Method, Fourth Edition, Mc Graw Hill, 1989; T.J.R.

Hughes: The Finite Element Method, Prentice Hall, 1987

Knowledge in mechanics and linear algebra