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Voltar para Método dos Elementos Finitos aplicado aos Problemas de Física

Comentários e feedback de alunos de Método dos Elementos Finitos aplicado aos Problemas de Física da instituição Universidade de Michigan

512 classificações

Sobre o curso

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

Melhores avaliações


12 de mar de 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.


4 de set de 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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51 — 75 de 96 Avaliações para o Método dos Elementos Finitos aplicado aos Problemas de Física

por 张宇杰

13 de ago de 2020

The course is arranged perfectly. I learned a lot through the coding assignment!

por Elizabeth F

5 de jul de 2018

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

por Harsh V G

7 de dez de 2017

excellent course , explains stuff right from the basics.

great job overall !!

por chtld

11 de mar de 2018

I think this course is very good for the students who first learn the fem.

por MOHD. F

19 de jun de 2017


Need to invest a great deal of time to understand thoroughly.


26 de mai de 2020


por LO W

31 de ago de 2019

It is worth to put some effort on this course. I learn alot .

por Prasanth s

12 de jul de 2017

thank you sir for giving this offering of this course

por Ann T

9 de abr de 2020

Very good course, I liked everything.

por Xi C

2 de jan de 2019


por Bhargav E

22 de set de 2017

Great we can learn many things


9 de jul de 2017

very friendly to the students


16 de set de 2018

The needful course for me

por Houssem C

16 de set de 2018

very interesting course

por Akash S

30 de jul de 2020

Excellent Teaching


14 de abr de 2017

good for learning.

por Salvatore V

30 de jan de 2021

very good course

por Mukunda K

7 de jan de 2020

Great Lecture.

por Junchao

30 de out de 2017

Great Course !

por Rahul S

13 de jun de 2018

It's awesome.

por Ramy F

4 de set de 2022

very good

por Induja P V

21 de out de 2020


por Marco R H

23 de jun de 2019

nice one!


9 de jul de 2017



24 de mar de 2022