## Lecture Finite Elements

### Prof. Dr. Vincent Heuveline

**Moodle:** Please check the moodle platform for more detailed information: Moodle Link FEM

**Schedule / Location:**

- Tue. 16:00-18:00 c.t. (c.t. means Cum Tempore, i.e. start at 16:15 ! ) / SR C Mathematikon, INF 205
- Fr. 11:00-13:00 c.t. / SR C Mathematikon, INF 205

**Organization of the lectures**: In preparation and to be announced

**Content of the lecture**

This lecture is an introduction to the finite element method (FEM) as a general and very powerfull technique for the numerical solution of partial differential equations in science and engineering. The focus is on mathematical and numerical analysis of the FEM. We consider in that context several important applications to problems from various areas.

- Abstract formulation of the finite element method for elliptic problems
- Approximation theory for FEM
- Derivation of specific finite element spaces
- Interpolation and discretization error
- Direct and iterative methods for solving linear systems occuring in FEM
- FEM Parabolic problems
- Implementation of the finite element methods
- A posteriori error estimates and adaptive meshes
- Mixed finite element methods

**Literature**

- Ern, Guermond: Theory and Practice of Finite Elements, 2010.
- Sashikumaar, Tobiska: Finite Elements: Theory and Algorithms, 2017.
- Braess: Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanic, 2007

**Requirements to attend this lecture**

This lecture is mostly self-contained. A background in numerical analysis e.g. introduction to numerical analysis is surely wellcome in order to understand the theoretical aspects of this lecture.

**Exam Modalities**

Regular participation in the lecture, successful participation in the exercises (reaching 50% of the points) and passing the final exam (90 min.).

**SWS:** 4

**ECTS:** 8 (Lecture + Exercices)

**Language:** English