Math Subjects that are prerequisites to Finite Element Method

Question

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

Answer 1

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

Answer 2

Courses

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

• Peruse the web for notes
• Find software that has various implementations and learn to use it
• Look in your local college library for books that interest you as well as others on the web
• Look at Open Courseware like at MIT, check out the videos and lecture notes
• Check out other open courses like http://www3.open.ac.uk/study/postgraduate/course/t884.htm
• Check the prerequisites at the school you want to take this at and see where you are in relation to those
• MSE Book Recommedations and resources to study PDE from and How to use FEM to solve a PDE

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