Finite Element Method Explained in 3 Levels of Difficulty

The finite element method is difficult to understand when studying all of its concepts at once. Therefore, I explain the finite element method in three levels with increasing complexity. At each level, different shape functions are introduced for discretizing the solution function of the given differential equation. At the first level, the shape functions are defined globally. At the second level, the shape functions are defined at the element level. And at the third level, the shape functions are defined on a reference element. Along the way, the concepts of assembly, integration by substitution and Gaussian quadrature are explained.

0:00 Introduction
2:45 Level 1
19:37 Level 2
26:33 Level 3
38:21 Summary

Keywords: finite element method, finite element analysis, partial differential equation, Poission problem, weak formulation, discretization, assembly, isoparametric concept, reference element, Gaussian quadrature

Music: Swans In Flight - Asher Fulero

[eduardoimaz]

In the first 20 minutes you already explained the FE way better than my proffesors could in an entire semester, thank you so much :)

[aqibrasheed]

Best explanation of FEM one could find on internet. Looking forward for more such videos on FEM.

[yondaimenamikaze]

By far the best Video on FEM that i could find !! Well structured and illustrated, thank you for the effort :)

[kialakungalgal]

Brilliant just brilliant. You are truly right, trying to understand every concept at once is difficult, but as you explain concept by concept it makes it so obvious. Thank you!! one of the best videos on this topic.

[Prashanth-ynzd]

This is the best. 4 months of the course is beautifully summarized in 40 mins!!
Please make a video on the Boundary element method if possible!

[eurosenelsuelo]

This is a great video. I won't be surprised when it eventually explodes within the Math & Eng communities. I'm definitely checking the rest of the videos from this channel.

[WalidBenKraiem]

By far the clearest explanation i ever seen. Thank you, I will save the video to send it to anyone will ask for what is FEM.

[eurosenelsuelo]

I am now taking a master's where one of the courses is FEM. I remembered this video and it was extremely helpful. I already said it months ago when I discovered the video but I'll say it again. THANK YOU for uploading this. I will share it with my class mates.

[carlosgiovanardi]

Great explanation! I found today this channel. Explained in an easy and understandable way. Congrats!!

[hannibal]

Omg best video on finite element ever. Ive only learn up to level 2 and got brief introduction to level 3 for structural engineering. This video give me better insight on the latter

[edspace]

The quality of your videos is insane, thanks a lot!!!

[mshriharikrishnan]

Amazing video with accurate animations! Thanks a lot, hope to see more such amazing videos from you.

[JavierMeseguerdePaz]

What a gem of a video! Best explanation I've seen of FEM in... Forever. Thank you very very much for this masterpiece.

[dgg]

Excellent video, thank you for your work and your time. Your pedagogy is really very good. It will surely be very useful to many people. Thank you very much.

[abcdefghijklm]

The explanation is so much more intuitive in this way. Beginning by explaining reference shape function and gaussian quadrature without having grasped the concept of what we're trying to do is so dumb. Thanks a lot, the video is so clear, the quality is crazy 🙏 Maybe one point that had me bugging because Linear algebra was quite some time ago is the fact N'(x)N't(x) define a matrix K s.t. Kij=n'i(x)n'j(x), I haven't tried but I think it can be demonstrated quite easily tho 👍

[cooler]

Thank you for your effort in making such an insightful video. More cheers to you. Waiting for more such videos from your channel

[arischai]

Thanks so much for your great effort in explaning the stuff beautifully.

[rezaafshar]

Very impressive!.. thanks a lot for sharing 🙏🙏

[bobbyshoemaker]

excellent video, will be showing my classmates

[andresyesidmorenovilla]

Brilliant explanation, thank you so much!