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有限元法在物理问题中的应用, 密歇根大学

261 個評分
57 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).


54 個審閱

創建者 Солин Виктор Александрович

Apr 02, 2019

Это отличный курс по МКЭ. Он не легкий, совсем нет. Я пытался пройти его больше года, но в итоге осилил. Он действительно помог мне разобраться в МКЭ.

This is exxelent course about FEM. It's not easy to complete. I've managed to finish it about year. It's very usefull. It hepled me to understand FEM.

Спасибо большое за эту возможность.

Thank you for this opportunity.

創建者 Abhishek Thakur

Mar 26, 2019

Very interesting course


Mar 17, 2019

An exceptionally created course with every detail of the subject matter. Thanks a lot.

創建者 Marvin Tiemessen

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.

創建者 Bowei "Bobbie" Wu

Jan 09, 2019

Thank you Prof. Garikipati and Greg for the amazing course. I have learned a lot about the FEM and am going to apply the knowledge to my research project.

創建者 chenxi

Jan 02, 2019


創建者 Vinayak Varma

Dec 30, 2018

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

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.