Partial differential equations play an outstanding role in engineering sciences and applications. The Maxwell equations for electromagnetic fields, the Navier-Stokes equations for fluids or the equations from elasticity theory are only a few examples. To solve such equations the finite element method is often used in practice. In this lecture, we present the necessary foundations for using the finite element method. We introduce the fundamental theory but above all the participants will implement important application examples using open source software and will learn practical aspects of the finite element method in this manner.

We start with a modern formulation of the finite element method and study how the method can be applied to engineering problems. We focus on example problems like the heat equation and the Maxwell equations which the participants will solve numerically. For the implementation of the numerical solutions we rely on open source software for the Python programming language. Additionally, we also take a look at aspects like mesh generation, time-dependent solutions and convergence.

Individual appointment of oral examination!