Finite Element Method

This video explains how Partial Differential Equations (PDEs) can be solved numerically with the Finite Element Method. For more information on this topic please check out Prof. Wick's lecture notes on "Numerical Methods for Partial Differential Equations":

----- Timestamps -----

00:00 Intro
00:11 Motivation
00:45 Overview
01:47 Poisson's equation
03:18 Equivalent formulations
09:56 Mesh
10:20 Finite Element
11:02 Basis functions
14:02 Linear system
15:53 Evaluate integrals
19:42 Assembly
21:17 Numerical quadrature
23:44 Master element
25:42 Solution
26:42 Mesh in 2D
27:15 Basis functions in 2D
28:37 Solution in 2D
29:04 Summary
29:53 Further topics
32:10 Credits

Created by:
Julian Roth & Max Schröder
Corrected by:
Jan Philipp Thiele & Thomas Wick
Translated to Spanish by:
Gina Kleinsteinberg

[SinaAtalay]

OMG! I really cannot express how thankful I am 🙏. This is a fantastic contribution to the community.

[cedrickhayat]

Thanks ! I have been looking for such a clear and detailed explanation for a long time. Either too simplified in 10' visuals or too obscure 2h lectures. This is just the golden mean. I will now dig into more détails with this good overview.

[huuthinhnguyen]

This is very useful. The explaination is easy to follow and the animations are beautiful! Amazing job! Thank you so much!

[mentalisa]

Danke dir! Das ist das erste Video auf YouTube, das mir wirklich hilft meine Vorlesung zu verstehen :) Toll aufgearbeitet und jeder Schritt gut und verständlich erklärt

[Pewpewlazorz]

Excellent, thank you for the time to put this video together. Also thank you for additional information on the lecture notes. Looking forward to see more on this.

[muaddib]

I would love some more videos on numerical methods with examples! Thank you very much

[DrSimulate]

Awesome videos, Julian! 🥰 You inspired me to try Manim as well. Hope to see some followup videos on your channel. Keep it up!

[cooler]

Thank you. Would like to know more of such insights in advance topics of FEM

[EDEsouth]

First complete demonstration, thanks man

[farzinhosseini]

Thanks for describing slow. It's easier to understand.

[hoijanlai]

This is the best intro video to FEM ever!!! Huge thanks!

[MB-bskt]

Thank you very much! This is a very well made video! Big ups!

[abitofeverything]

thank you so much for the explaining it! Best resource I have seen on the material so far!!

[oumardeme-vk]

Excellent!! simple, clear. Thank you!

[최승훈-cx]

The way I see it in 25:17, RHS of the bottom integration's interval should be K(1) not Ki(hi).

[ananyapamde]

This is really beautiful. Thank you very much!

[emadmahmoud]

Thank you very much for this perfect tutorial 💐

[AndrewBeatcast]

This is an excelente video. I really strong recommend it. I fond of the way that you explained and the notation that you use it, very formal, but easy to understand.

[PafLeRenard]

Very good introduction ! Even if the part on "master element" is a a little fast for me...

[idiosinkrazijske.rutine]

Great explanation! Is this made using manim or similar technology?