Back to The Finite Element Method for Problems in Physics

4.6

stars

402 ratings

•

83 reviews

This course is an introduction to the finite element method as applicable to a range of problems in physics and engineering sciences. The treatment is mathematical, but only for the purpose of clarifying the formulation. The emphasis is on coding up the formulations in a modern, open-source environment that can be expanded to other applications, subsequently.
The course includes about 45 hours of lectures covering the material I normally teach in an
introductory graduate class at University of Michigan. The treatment is mathematical, which is
natural for a topic whose roots lie deep in functional analysis and variational calculus. It is not
formal, however, because the main goal of these lectures is to turn the viewer into a
competent developer of finite element code. We do spend time in rudimentary functional
analysis, and variational calculus, but this is only to highlight the mathematical basis for the
methods, which in turn explains why they work so well. Much of the success of the Finite
Element Method as a computational framework lies in the rigor of its mathematical
foundation, and this needs to be appreciated, even if only in the elementary manner
presented here. A background in PDEs and, more importantly, linear algebra, is assumed,
although the viewer will find that we develop all the relevant ideas that are needed.
The development itself focuses on the classical forms of partial differential equations (PDEs):
elliptic, parabolic and hyperbolic. At each stage, however, we make numerous connections to
the physical phenomena represented by the PDEs. For clarity we begin with elliptic PDEs in
one dimension (linearized elasticity, steady state heat conduction and mass diffusion). We
then move on to three dimensional elliptic PDEs in scalar unknowns (heat conduction and
mass diffusion), before ending the treatment of elliptic PDEs with three dimensional problems
in vector unknowns (linearized elasticity). Parabolic PDEs in three dimensions come next
(unsteady heat conduction and mass diffusion), and the lectures end with hyperbolic PDEs in
three dimensions (linear elastodynamics). Interspersed among the lectures are responses to
questions that arose from a small group of graduate students and post-doctoral scholars who
followed the lectures live. At suitable points in the lectures, we interrupt the mathematical
development to lay out the code framework, which is entirely open source, and C++ based.
Books:
There are many books on finite element methods. This class does not have a required
textbook. However, we do recommend the following books for more detailed and broader
treatments than can be provided in any form of class:
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, T.J.R.
Hughes, Dover Publications, 2000.
The Finite Element Method: Its Basis and Fundamentals, O.C. Zienkiewicz, R.L. Taylor and
J.Z. Zhu, Butterworth-Heinemann, 2005.
A First Course in Finite Elements, J. Fish and T. Belytschko, Wiley, 2007.
Resources:
You can download the deal.ii library at dealii.org. The lectures include coding tutorials where
we list other resources that you can use if you are unable to install deal.ii on your own
computer. You will need cmake to run deal.ii. It is available at cmake.org....

SS

Mar 13, 2017

It is very well structured and Dr Krishna Garikipati helps me understand the course in very simple manner. I would like to thank coursera community for making this course available.

RD

Sep 05, 2020

Well worth the time if you wish to understand the mathematical origin of the FEM methods used in solving various physical situations such as heat/mass transfer and solid mechanics

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By chenxi

•Jan 02, 2019

编程作业好评，如果能够出详细介绍dealii的系列就更好了。

By E B K

•Sep 22, 2017

Great we can learn many things

By NAGIRIMADUGU P

•Jul 09, 2017

very friendly to the students

By RAKSHITH B D

•Sep 16, 2018

The needful course for me

By Houssem C

•Sep 16, 2018

very interesting course

By Akash S

•Jul 30, 2020

Excellent Teaching

By NAGEPALLI N K

•Apr 14, 2017

good for learning.

By Mukunda K

•Jan 08, 2020

Great Lecture.

By Junchao

•Oct 30, 2017

Great Course !

By Rahul S

•Jun 13, 2018

It's awesome.

By Marco R H

•Jun 23, 2019

nice one!

By BHARATH K T

•Jul 09, 2017

good

By Krishnakumar G

•Aug 16, 2019

While quite mathematical in nature as opposed to a purely applied view of the method, Prof, Krishna Garikipati's teaching style and clear explanations make the material accessible to practicing engineers outside of academia. This is a great course to take for a strong introduction to the theory of FE method. The TA's explanation videos, while being helpful can sometimes be too verbose. This is a long course, and took me nearly 4 months to finish the videos. I had to go back and watch each of the videos at least 2 times over these 4 months, since some ideas are a bit mathematically dense. Upon second viewing, the ideas become clearer. Overall, a highly recommended course!

By Pierre B

•Mar 17, 2017

This is a good intro course which introduce the Finite Element Method step by step, which suited me perfectly since I hardly coded in c++ nor did FEM before.

Nevertheless, as a graduate student, the pace is very slow, and the outline and motivation unclear, which would likely have discouraged me if I did not review video in x2, and stuck to second week lectures and onward.

I would advise to introduce more outline and motivation at the beginning of the week lecture to keep students motivated.

Apart from that, I recommand the course !

By Georgi H S

•Aug 02, 2020

The course is a nice and well structured from theoretical point of view introduction to Finite Element Methods. The computational part is a little marginal in the course, but is the main for the grading. If the course had a perfect division between theory and computational part it would've been perfect. The only problem is that in theory, one does the same kind of calculations over and over again, and it's boring after few times.

By Marvin T

•Jan 15, 2019

In principle, it is a good course and taught in a very understanding manner. For a five star rating, I would like to suggest that there should be additional physics, e.g. convection problems, or turbulence, featuring a CFD chapter for example with heat transfer.

By Sri H M

•Nov 15, 2019

A good primer of the theoretical fundamentals of the Finite Element Methods. The coding assignments were good too but could have benefited more with support from the mentors via the forums.

By Antonio R

•Jun 21, 2018

The course is really deep and I have to say the professor really inspired me to keep learning.It might be a little slow but the course is in general pretty good.

By Vinayak V

•Dec 30, 2018

The course was was great. However, illustrative examples solving real engineering problems could be introduced in lecture.

By Kapouranis I

•Jun 29, 2018

Really recommend it. There will be times when you think you should give up, but just finish it. It is worth it.

By Guilherme D

•May 21, 2019

Well structured course. It builds up from the basics of finite elements to more complex problems.

By YAN B

•Dec 22, 2019

Good content, not easy for beginners. It may take much longer to fully understand the content covered in the lecture.

Programming exercise is somehow difficult as you have to watch dealIii tutorial videos on YouTube yourselves.

One particular drawback is that the presentation skill of the instructor should be improved as there are a lot of repetitive unnecessary and redundant writing and explanation.

By John F S

•May 31, 2019

Okay for learning the basics of FEM outside of a real clasroom setting. Focused too much on using their own software for actual FEM analysis. I understand that creating an actual FEM from scratch is too much to ask for an online course, but a lot of their program isn't well documented and detracts from the learning experience.

By George K

•Jan 22, 2020

You will need much more time than the time listed (expectation time listed). Although you can learn

a lot!!!!! I feel grateful!

By LINGALA K

•Jul 13, 2017

the course is enough learn things better way to explain give notes and pdf format and doc l.

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