FEM for Solving PDEs: Beginner Textbooks & Fluid Flow

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Discussion Overview

The discussion centers on finding introductory textbooks for solving partial differential equations (PDEs) using finite element methods (FEM), with a particular interest in applications to fluid flow problems. Participants share recommendations and express their preferences for different numerical methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for beginner-level textbooks on FEM for PDEs, specifically for fluid flow applications.
  • Another participant suggests considering finite volume methods for fluid flow instead of FEM.
  • A different participant expresses a preference for FEM over finite volume methods, citing their research needs in rotating flows and a dislike for commercial CFD packages.
  • Several participants recommend the book "Spectral/hp methods for computational fluid dynamics" by Karniadakis and Sherwin, noting its practical approach and various features.
  • Classic texts by Zienkiewicz & Taylor and Strang & Fix are mentioned, though their current relevance is questioned.
  • A suggestion is made to refer to a paper on implementing FEM in MATLAB, highlighting a practical resource for immediate application.
  • One participant challenges the reasoning behind choosing to program a custom FEM, suggesting that a commercial finite volume solver might be more efficient for research purposes.

Areas of Agreement / Disagreement

Participants express differing views on the suitability of finite element methods versus finite volume methods for fluid flow problems. There is no consensus on the best approach, as some advocate for FEM while others recommend finite volume methods.

Contextual Notes

Participants' preferences are influenced by their individual experiences and research requirements, leading to a variety of perspectives on the choice of numerical methods. The discussion reflects a range of assumptions about the capabilities and limitations of FEM and finite volume methods.

RobosaurusRex
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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.
 
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DrClaude said:
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!
 
I like the book "Spectral/hp methods for computational fluid dynamics" by Karniadakis and Sherwin.
 
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the_wolfman said:
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
 
DrClaude said:
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.

RobosaurusRex said:
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.
 

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