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

2017年3月12日

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

2020年9月4日

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

篩選依據：

創建者 YAN B

•2019年12月22日

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.

創建者 John F S

•2019年5月31日

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.

創建者 George K

•2020年1月22日

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

a lot!!!!! I feel grateful!

創建者 LINGALA K

•2017年7月13日

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

創建者 Congyi L

•2018年1月28日

Not clear on AWS setup. Easy get confused

創建者 Murali R

•2017年1月24日

good for improving skills

創建者 SACHIN K

•2020年6月5日

good exprnce

創建者 M M K R

•2017年7月9日

good

創建者 Patrick H

•2017年12月15日

In my opinion the course material is a good base but needs further development.

This includes new recordings of old lectures which contain errors. Sometimes there is a correction video included directly in the lecture video with an additional correction video and same content placed afterwards in the timeline.

Also there should be updated version of coding assignments. As stated in the forum it was just possible to pass one assignment by 100 percent if a deal.ii version from 2015 is used. However, the provided link to the deal.ii VM provides a recent version 2017. When run the same code on the student computer with deal.ii from 2015 one could get full marks. However, using the recent version from 2017, the automatic grading just gave 80 percent. This should be for sure improved.

Additionally I would suggest to make a more even work distribution for each week. There are weeks with just 3 hours of videos and other weeks with up to 9 hours. It would be beneficial if that could be more balanced.

Coding assignment 1 is placed with a deadline in week 3. However, the required material for passing this is taught in week 4 and 5. Therefore, I would suggest to push CA1 to week 5.

創建者 Mehmet A Ö

•2018年4月30日

Lecturer expresses anything at a snail's pace. He is really a slowcoach.

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