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Finite Element Methods for Flow Simulations

Lecturer:D. Arndt
Class data: Tue/Thu 11-13h, Mathematikon (INF 205), SR11
Start: October 17, 2017


Due to the ubiquity of fluids, the simulations of flow problem is of great importance in many applications: Examples include the design process of new aircraft or cars, simulations of air flow in the interior of buildings, simulation of the natural convection in the earth’s mantle, simulation of fusion reactors or understanding the dynamo effect in astrophysical bodies. The simulation of all these phenomena in experiments is often very complicated and expensive. Hence, there is an increasing desire to perform numerical simulations be it to complement the experiments or to replace them.

This lecture will focus on mathematical tools and techniques for suitable discretizations of flow problems. In particular, we will consider existence and uniqueness theory for convection-diffusion problems, the Stokes-, Oseen- and Navier-Stokes equations both on the continuous and on the discrete level.
The course will mainly follow H.-G. Roos, M. Stynes, L. Tobiska: Robust Numerical Methods for Singularly Perturbed Differential Equations - Convection-Diffusion-Reaction and Flow Problems but we will also consider some extensions like pressure-robust error estimates, grad-div stabilization and stabilizations restoring inf-sup stability.


The course requires a basic understanding of finite element discretizations for partial differential equations such as taught in the lecture "Numerik partieller Differentialgleichungen". Knowledge about mixed finite elements methods is favourable but not strictly required. We will do some recapitualtions in the first few lectures.




Homework problems

  1. Exercise Sheet 1