Approximate Solutions - The Galerkin Method

Finding approximate solutions using The Galerkin Method. Showing an example of a cantilevered beam with a UNIFORMLY DISTRIBUTED LOAD.

Governing Equations: Weak Forms vs Strong Forms:

The Ritz Method:

0:00 Introduction
1:00 The Method of Weighted Residuals
8:14 The Galerkin Method - Explanation
13:37 Orthogonal Projection of Error
20:49 The Galerkin Method - Step-By-Step
23:26 Example: Cantilever beam with uniformly distributed load using Galerkin's Method - Shape Functions
28:53 Example: Cantilever beam with uniformly distributed load using Galerkin's Method - Solving for the Constants
31:22 Example: Cantilever beam with uniformly distributed load using Galerkin's Method - Solution
32:57 Quick recap

[pauloedmachado]

Nice video, but I just don't get how the load f(x) was taken out of the integral as a constant, if it's a function of x

[hnrwagner]

best explanation I have ever seen on Galerkin Method

[jimmypostwala]

You saved so much of my time … I heard my professor for weeks strong form weak form …. Dint understand at all what is he tryna accomplish…. What a breadth of fresh air !

[iuryt]

I am really impressed on how pedagogical this is

[blackguardian]

The day just become better! A long waited video and I hope that there will be many more! Thank you!

[paulbytheriver]

thanks, excellent presentation with good insights.
i actually derived to what amounts to the same approach many years ago, without the mathematical background using least squares curve fitting to a known function integrating over the domain instead of discrete points. rationalizing that to minimize the error in each coefficient meant finding partial derivatives in the approximating function. forms a set of linear equations.

[delfipotters]

Incredible video. I have been searching through textbooks to find an explanation for why we would want our basis functions to be orthogonal to the residual, and I couldn't find anything. Thank you so much. I understand the concept so much better now.

[nickgenin]

the best video on this topic here in YouTube. Great job, professor. You make it so clear and really easy to understand

[xino]

I really really should search explanations in YouTube, I needed this 3 weeks ago for my finals!

[JavArButt]

Now I understand what I was reading for some time - thank you for this lecture

[omarsaleem]

Your Videos are awesome.
I spent this weekend watching and applying the tutorials in which you explained coding by python.
I can't find the right words to describe how much I'm impressed with your work. Thanks a lot for your efforts and time and I hope you will add more in the direction of python coding.

[TarshitSehgal]

crystal clear explanation, u r a really good teacher!!

[kenankenan]

Your explanation methods your approach is brilliant!!! Thank you dear professor!

[lujqian]

Very nice video and the great lecturer. Explained clearly. Thanks a lot.

[POPO-kknh]

Fantastic explanation!!! I couldn't resist waiting for the end of the video to leave a comment. It couldn't be more explicit and I REALLY needed to learn this method. Thank you very much.

[johnsmithsu]

Explanation was Awestruck!!! I hope in future video you will share us about explanation and problem solving Space Frame 🙏

[uqyge]

brilliant.every stem student should take a look. best on garlerkin method

[behzadtaghipour]

Thanks alot! specially the explanation of the concept of orthogonality. that was what i was looking for great job!

[AmericanDream_VNPride]

Thank you Sir! This is a beautiful explanation that I could not ask for more. It clears my mind and give an aha moment! Salute.

[zillenjunge]

The reference to the weighted residuals was really helpful. Interesting generalization of collocation and least squares methods, which were familiar to me.