LFU:online

Department of Mathematics Department of Mathematics, Pedagogical University Vorarlberg Pedagogical University Vorarlberg

Dr. Christoph Erath Dr. Christoph Erath

921014

6xxxxx2B24
(Pedagogical University Vorarlberg)

LV Interdisciplinary Skills

VO 2

5

not applicable

not applicable

German

description of models which leads to PDEs; classification of PDEs - elliptic, parabolic, hypberbolic; solving PDEs; analytical studies; numerical solving of PDE with the finite difference methods (FDM) and the finite element method (FEM); Numerical analysis; Possible integration of some parts of the lecture in school lessons

Nowadays, mathematical models can be found in all areas of life. Especially in engineering and natural science, processes are often described with partial differential equations (PDE for Partial Differential Equation). This lecture provides an overview of the mathematical theory of PDEs. A rigorous description is given. In the following, we will examine (analytically) so-called elliptical PDEs more closely. Very often PDEs for practical problems cannot be solved analytically. Therefore, we consider two numerical methods: the finite difference method (FDM) and the finite element method (FEM). The FEM in particular is widely used in industrial simulation codes. Practical examples (1D) show the great potential of PDEs, which are indispensable in today's modern simulation world. A possible integration of the acquired knowledge in school lessons (upper level) is discussed.

-Brenner, Scott: The Mathematical Theory of Finite Element Methods (Springer 2008) -Braess: Finite Elemente (Springer 2003) -Steinbach: Numerical Approximation Methods for Elliptic Boundary Value Problems (Springer 2010)

basic courses in mathematics, in particular Analysis 1, Analysis 2, and linear algebra. The lecture Applied Mathematics is recommended