Graduate FEM for Solving PDEs: Beginner Textbooks & Fluid Flow

[RobosaurusRex]

Hi, my background is in mathematics, and theoretical physics.
I am new to the realm of solving PDEs using Finite element methods, does anyone know of any good introductory level textbooks for course notes?

I had a poke around online and couldn't find anything overly useful.

Also I am interested in solving fluid flow problems with this method :)

Thanks.

 

[DrClaude]

Have a look at https://books.google.se/books?id=Pl5zMAEACAAJ

If you are going to study fluid flow, I really recommend you consider finite volume methods instead.

 

[RobosaurusRex]

Have a look at https://books.google.se/books?id=Pl5zMAEACAAJ

If you are going to study fluid flow, I really recommend you consider finite volume methods instead.

That's not really an. Option for me. I am not a fan of commercial cfd packages, and I do not enjoy or understand coding my own numerics in finite volumes. I use open foam for my finite volume needs. My research in rotating flows requires me to write my own numerics, and finite element is how I wish to do this. Thanks for the comment though!

 

[the_wolfman]

I like the book "Spectral/hp methods for computational fluid dynamics" by Karniadakis and Sherwin.

 

[bigfooted]

I like the book "Spectral/hp methods for computational fluid dynamics" by Karniadakis and Sherwin.

A very nice book. I liked the practical approach, dealing with the numbering of the arrays, the treatment of the Schur method and the different PDE types.
The website for their code is here: http://www.nektar.info/

The classic books are by Zienkiewicz & Taylor and Strang & Fix. I remember reading them years ago, I'm not sure if they are still considered up-to-date.

If you want some immediate action, you could try this paper on how to implement FEM in 50 lines of matlab:
https://www.math.hu-berlin.de/~cc/cc_homepage/download/1999-AJ_CC_FS-50_Lines_of_Matlab.pdf

 

[bigfooted]

If you are going to study fluid flow, I really recommend you consider finite volume methods instead.

Maybe 'as well' and not 'instead'?
Finite element methods have evolved to something more powerful than you can possibly imagine.

That's not really an. Option for me. I am not a fan of commercial cfd packages, and I do not enjoy or understand coding my own numerics in finite volumes. I use open foam for my finite volume needs. My research in rotating flows requires me to write my own numerics, and finite element is how I wish to do this. Thanks for the comment though!

'Not being a fan of commercial cfd packages', 'Not understanding finite volumes', and 'wishing to do finite elements' is not really solid reasoning to choose to program your own finite element method. If your goal is to research rotating flows, then a commercial finite volume solver is probably your best choice to achieve this: You don't have to worry about coding, numerical methods, bug hunting, etc. Other people have done that for you 15 years ago.