I want to Learn Finite Element Method. What are the Math Subjects that are prerequisite to FEM?

I am a mechanical engineer. FEM was not taught to us in College. :(

I am profficient in Engineering Mechanics, Differential Calculus, Integral Calculus and Basics of Differential Eequations. I also know Matrix manipulations. I understand Fourier Series, Fast Fourier Transform and Basic of Laplace Transform. In the past I have knowledge in Runge-Kutta, Stokes Theorem, Gradient, Divergence and Curl. I can derive the Navier-Stokes Equation.

What other math subject do I need to learn before I study Finite Element Method? Can you suggest online course for FEM (other than MIT OCW)?

Thank you very much. Joseph


migrated from mathoverflow.net Jul 19 '13 at 4:01

This question came from our site for professional mathematicians.

  • 1
    $\begingroup$ I have flagged your question to be moved to math.stackexchange. This forum is for research into mathematics (i.e. developing new mathematics, rather than learning old mathematics). $\endgroup$ – Ryan Budney Jul 19 '13 at 3:14
  • $\begingroup$ WHy don't you just pick up some book on FEM (Ciarlet is good), and see if you can understand it. If yes, great, if not, go read what you are missing. $\endgroup$ – Igor Rivin Jul 19 '13 at 3:29
  • $\begingroup$ What specific equation you are interested in applying FEM on? $\endgroup$ – Shuhao Cao Jul 19 '13 at 4:06


The primary classes you are going to want to have include:

  • Complex Analysis
  • Differential Equations (both Theory and Numerical variants and several of each)
  • Partial Differential Equations (both Theory and Numerical variants and several of each)
  • Numerical Analysis Courses
  • Some Programming would not hurt
  • An algorithms and Computational Complexity course would not hurt

Other Recommendations

From all of this, you might be better able to gauge where you are and what you are deficient in.

  • $\begingroup$ Thank you very much for your inputs. I greatly appreciate it. $\endgroup$ – Joseph Roxas Jul 19 '13 at 10:01
  • $\begingroup$ @JosephRoxas: You are very welcome! Regards $\endgroup$ – Amzoti Jul 19 '13 at 14:14
  • $\begingroup$ Excellent list of references! +1 $\endgroup$ – Namaste Jul 19 '13 at 15:04
  • $\begingroup$ Yes, indeed, happy POETS Day! Enjoy yours ;-) $\endgroup$ – Namaste Jul 19 '13 at 15:18

It is really hard to list a pre-requirement for a course like FEM. This is partly because it is thought in many different flavours. If you don't care about the maths in FEM, a basic knowledge of calculus, ODE and linear algebra should suffice. I think that is the level required if you look at the MIT open course ware page. There are many books with engineering flavor on FEM. FEM by Logan and the book by Bathe are such two books.

If you really want to learn FEM from a mathematical point of view, it will be useful to know a bit of analysis, calculus of variations and functional analysis. But this might be a lot for you to learn and I don't know how invested you are to learn FEM in its full glory. I recommend, as Igor pointed out, to take a look at Ciarlett. A very introductory but mathematical point view on FEM is available here http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CCsQFjAA&url=http%3A%2F%2Fwww.math.umn.edu%2F~olver%2Fnum_%2Flnf.pdf&ei=bbzoUfboHIHD4AP-1YHYBg&usg=AFQjCNFN1mBCn9b2eeBzrpLUK1j3LOlh-Q&sig2=SJrqngdqQ-HDBiRrESysaQ&bvm=bv.49478099,d.dmg. Then you can see what you are missing as you read and assess your level of preparedness for the course. cheers, abiyo

  • $\begingroup$ Thank you very much for your inputs. I greatly appreciate it. $\endgroup$ – Joseph Roxas Jul 19 '13 at 10:00

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