Back to The Finite Element Method for Problems in Physics

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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

Mar 12, 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.

RD

Sep 4, 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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By Rohan S

•Jan 21, 2017

Professor Garikipati provides a thorough explanation which is of immense help to a beginner in FEM like me. The course is very interesting! The practice of making entire video in form of notes is very efficient for a student to grasp everything the teacher wants to convey.

By Josiel C T

•Nov 30, 2020

The course was very interesting and helped me to understand the mathematical basis of the Finite element method. Besides, Professor Krishna Garikipati makes the concepts very easy to understand. Due to this course, I am very motivated to go through more advance topics.

By 杨名

•Jul 7, 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.

By Gabriel D L C

•Apr 27, 2021

Excellent course on the foundations of the Finite Element Method. The mathematical concepts are very well presented so that it enables the learners to use current finite element software consciously without facing it as a black box.

By Patel P

•May 21, 2020

Professor is very clear with explanation, and meticulous with accuracy to the highest degree possible. Assignment at first seems daunting, but Gregory Teichert explains very clearly and then it seems like only a typing job.

By pavankumar j

•Jun 16, 2021

An exceptional course for people pursuing career in Mechanical Engineering and need a deeper understanding of Finite Element Method fundamentals. Huge respect for Sir Krishna Garikipati for the kind simplified explanation.

By DILAN T S

•Oct 19, 2020

I got the fundamental knowledge of the finite element method also experienced C++ programming for simulating a simple system using the finite element method. Course content and programming is interest to me.

By Asan

•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.

By Matthijs S

•Jul 11, 2017

Well-structured course with high quality lectures and slides in Galerkin FEM for problems in physics. A 'Must Take' to every professional in computer-aided design for research and concept development.

By Michael B

•Mar 5, 2017

This was a great course, I can only recommend. The tutor really explains basically all that there is to linear PDEs. What I miss, maybe as a different course is the case of nonlinear equations.

By Rahul B D

•Sep 5, 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

By 杨思超

•Aug 30, 2019

very good course on explaining the mathematical ground of FE and connecting it with the physical domain. Also learned a lot on the coding part of the FE modeling

By MEHMET A

•Sep 8, 2020

This course is really didactic course. If you are interested in FEM, please take this course. Thank you Professor Krishna Garikipat.

Sincerely....

By Eik U H

•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.

By Francisco T

•Jan 13, 2018

This is a very good course for getting introduced in the theory and practice of the finite element method. I wish there were a second part.

By Sumedh S

•Nov 23, 2020

Excellent course, subject matter is presented very methodically, and the instructor's command over the subject taught is outstanding.

By Devara s

•Jul 10, 2017

it is good course it more useful to us and i learn lot information for this course thanking you giving for this opportunity

By Aamir I

•Mar 9, 2017

A rigorous and organized introduction to the subject with the additional benefit of learning through implementation.

By LUIS A P C

•Sep 17, 2020

This should be the standard way for teaching Finite Element Methods in Engineering in colleges and universities

By benjamin j d o

•Jun 29, 2017

Absolutely amazing¡¡ Where is the other course in continuum physics in MOOC format? I can't wait.

By Diego V

•Mar 24, 2021

Excelente para personas con conocimiento básico o nulo de elementos finitos. Super recomendado :)

By Angelos M

•Feb 14, 2021

Perfect Course !

I recommend it to everyone who is interested in mathematics and physics.

By Brad R

•Mar 12, 2020

Very well organized and presented from an instructor who is clearly quite knowledgeable.

By ISAAC T

•Jul 29, 2017

Incredibly instructive, even for an industrial engineer especialzed in mechanic like me.

By Deepak P

•Mar 17, 2019

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

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