Chevron Left
返回到 有限元法在物理问题中的应用

學生對 密歇根大学 提供的 有限元法在物理问题中的应用 的評價和反饋

449 個評分
93 條評論


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



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.


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


76 - 有限元法在物理问题中的应用 的 90 個評論(共 90 個)

創建者 Marvin T


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 Sri H M


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.

創建者 Antonio R


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 Vinayak V


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

創建者 Kapouranis I


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 Guilherme D


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

創建者 YAN B


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


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


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

a lot!!!!! I feel grateful!



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

創建者 Congyi L


Not clear on AWS setup. Easy get confused

創建者 Mk R


good for improving skills



good exprnce

創建者 M M K R



創建者 Mehmet A Ö


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