# Advanced Finite Element Methods for MHD (MA4303)

The lecture will be devoted to advanced Finite Element discretisation of partial differential equations.
We will first introduce general Finite Element spaces beyond Lagrange Finite Elements in the framework of of the Finite Element Exterior Calculus introduced by Arnold, Falk and Winther.
We will also introduce the Discontinuous Galerkin method and the concept of isogeometric analysis.
As an application of these methods, we will consider the linear and nonlinear magnetohydrodynamics (MHD) equations applied to magnetic fusion problems that we will derive at the beginning of the lecture.

An exercise class is associated to the lecture where as well analytical exercises as coding exercises in Matlab will be proposed.

## Lecture notes

Version of January 30, 2017 of the

lecture notes
## News

- Lecture on Finite Element Exterior Calculus starts on December 19

## Literature

- A. Ern and J.-L. Guermond: Theory and Practice of Finite Elements, Springer 2004.
- D. Di Pietro and A. Ern: Mathematical Aspects of Discontinuous Galerkin Methods, Springer 2012.
- D. Arnold, R. Falk, R. Winther: Finite Element Exterior Calculus, from Hodge theory to numerical stability, Bull. AMS, vol 47 (2), pp. 281--354 (2010)
- J.P. Freidberg: Plasma physics and fusion energy, Cambridge University Press (2007)
- D. Schnack: Lectures in Magnetohydrodynamics, Springer (2009)

## Lecturers

- Lectures: Prof. Dr. Eric Sonnendrücker. Monday 8:30-10:00. Room 03.06.011
- Exercises: Dr. Stefan Possanner. Monday 10:15-11:45 (every two weeks). Room 03.04.011

## Exercise sheets

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EricSonnendruecker - 20 Jul 2016