Finite Element Methods for Flow Simulations
Lecturer:  D. Arndt 
Class data: 
Tue/Thu 1113h, Mathematikon (INF 205), SR11


 Start: October 17, 2017 
Module  MM35 
Summary
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 earthâ€™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 convectiondiffusion problems,
the Stokes, Oseen and NavierStokes 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  ConvectionDiffusionReaction and Flow Problems
but we will also consider some extensions like pressurerobust error estimates, graddiv stabilization and stabilizations restoring infsup stability.
Prerequisites
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.
Announcements
 On November 07, 2017 we will be in SR12.
Schedule
 October 17: Notation, Modelling of flows, Transport theorem, Cauchy Theorem
(3.3 The Cauchy Stress tensor)
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 October 19:
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 October 19: Conservation Laws, Basic equations of fluid dynamics
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 October 24:
 October 26:
 October 31: holiday
 November 02:
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 November 07: shifted
 November 09: shifted
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 November 07:
 November 09:
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 November 14:
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 November 30:
 December 05:
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 December 12:
 December 14:
 December 19:
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 January 09:
 January 11:
 January 16:
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 January 30:
 February 01:
 February 06: Oral exams
 February 08: Oral exams
Literature
Homework problems
 Exercise Sheet 1