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

SWS: 4

ECTS: 8 (Lecture + Exercices)

Language: English

Organization of the lecture

As long as face-to-face events are suspended at the university, this lecture will only be held online. The corresponding lecture materials in the form of videos, slides, etc. will be uploaded in this platform. The forum can be used for questions, comments and discussions.

Schedule: We. and Fr., 11:00 bis 12:00 c.t. (c.t. means Cum Tempore, i.e. start at 11:15 !!! )

Location: Lecture Hall Cantor (Audimax-heiCONF)

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.).