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The Finite Element Method for Problems in Physics, University of Michigan

223 個評分
50 個審閱


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 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


創建者 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.

創建者 YW

Jun 21, 2018

Great class! I truly hope that there are further materials on shell elements, non-linear analysis (geometric nonlinearity, plasticity and hyperelasticity).


47 個審閱

創建者 Houssem Chkili

Sep 16, 2018

very interesting course


Sep 16, 2018

The needful course for me

創建者 杨名

Jul 07, 2018

Very detailed explanation and illustration. The Professor will help you revise the course material at the beginning of each video, so don't worry about forgetting things. The course is interesting and useful. Gain me a lot of insights. Assignments are great.

創建者 Elizabeth Flores

Jul 05, 2018

I like this course it is useful because have theory and the application part.

創建者 Kapouranis Ilias

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.

創建者 Yuxiang Wang

Jun 21, 2018

Great class! I truly hope that there are further materials on shell elements, non-linear analysis (geometric nonlinearity, plasticity and hyperelasticity).

創建者 Antonio Rios

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.

創建者 Rahul Soni

Jun 13, 2018

It's awesome.

創建者 Eik Uwe Heine

May 26, 2018

Looking backward from the end of this course I know, whatever I felt during the last months, this course is really great. Thank you very much.

創建者 Asan Adamanov

May 15, 2018

Thank you very much that you helped me understand of the FEM. I'm so happy that I could find your online course.

You did a really very significant course which help to people easily fıgure out the FEM.