FEM for Solving PDEs: Beginner Textbooks & Fluid Flow

In summary, a person with a background in mathematics and theoretical physics is looking for an introductory level textbook on solving PDEs with Finite element methods. After searching online, they received a recommendation for the book "Spectral/hp methods for computational fluid dynamics" and a paper on implementing FEM in Matlab. They also discussed the option of using finite volume methods for studying fluid flow, but the person stated their preference for finite element methods due to their research in rotating flows. They also mentioned not being a fan of commercial CFD packages and not understanding finite volumes as reasons for choosing to program their own finite element method. However, it was suggested that a commercial finite volume solver may be a better option for their research.
  • #1
RobosaurusRex
29
1
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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  • #3
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!
 
  • #4
I like the book "Spectral/hp methods for computational fluid dynamics" by Karniadakis and Sherwin.
 
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  • #5
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
 
  • #6
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.
 

FAQ: FEM for Solving PDEs: Beginner Textbooks & Fluid Flow

1. What is FEM and how does it work?

FEM (Finite Element Method) is a numerical technique used to solve partial differential equations (PDEs). It involves dividing a complex problem into smaller, simpler elements, and then using mathematical equations to approximate the solution for each element. These element solutions are then combined to obtain an approximate solution for the entire problem.

2. Can FEM be used to solve any type of PDE?

Yes, FEM can be used to solve a wide range of PDEs, including elliptic, parabolic, and hyperbolic equations. It is especially useful for problems with complex geometries or boundary conditions, which may be difficult to solve using traditional analytical methods.

3. What are some common applications of FEM in fluid flow?

FEM is commonly used in fluid flow simulations to model and analyze various industrial and natural processes, such as aerodynamics, heat transfer, and groundwater flow. It is also used in the design and optimization of structures such as aircraft wings, car bodies, and pipelines.

4. Are there any limitations or challenges associated with using FEM for solving PDEs?

One of the main challenges of FEM is its computational complexity, which can require a significant amount of time and resources to solve large and complex problems. Additionally, the accuracy of the solution can be affected by the choice of element size and shape, and the quality of the mesh used to discretize the problem.

5. What are some recommended beginner textbooks for learning FEM for solving PDEs?

Some popular and highly recommended beginner textbooks for learning FEM for solving PDEs include "An Introduction to the Finite Element Method" by J.N. Reddy, "Finite Element Procedures" by K.J. Bathe, and "The Finite Element Method: Linear Static and Dynamic Finite Element Analysis" by T.J.R. Hughes.

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