Students should understand mathematical models in engineering and applications and learn how to choose proper numerical methods for them.

In the first part of the lecture we derive mathematical models in fluid dynamics, solid mechanics, and electromagnetics. These models will be simulated using the finite element package Netgen/NGSolve developed at the institute. In the second part, we discuss proper versions of the finite element method for these applications. The methods include mixed finite elements to satisfy divergence free constraints, discontinuous Galerkin methods for convection dominated problems, and vector-valued elements for discretizing exact sequences. In the exercises, students will replace some pieces of the code. Students will work in teams.

No lecture notes are available.

Prerequisites are Numerical methods for Differential Equations , or basic knowledge of the finite element method from other classes. Some experience in C++ is helpful.