So it is possible to understand it without being bogged down and frustrated by unnecesarry maths. Very simple and concise. This is something that everyone should understand before trying to understand the numerical approach. Thanks a lot ;)
After reading multiple books by, e.g., Belytschko and Zienkiewicz, I finally understood the problem thanks to your video. Thank you VERY much. PhD thesis, here I come.
Very well that you chose the right weighted function! I am looking - researching topic of Isogemetric and how Galerkin as localized function has an optimal convergence rate for head and velocity. If give meassure of the head = (x+1) than velocity will be only x. We also apply Fup or B-splines. However, Galerkin in isogemetric has the most expensive isogomeric concept due to numerial integration what we have seen in yours presentation especially if we put the conducte matrix. Applying yours IGA framework with classicl Galerkin what you explained briefly and clearly and add the collocation in same Galerkin we can get formulation of groundwater structure and flow! Thans how you contribute to isogomeric topic to the groundwater flow with applying anylitic approach. We have point how to exact did it in geometry with resolution level and spline based methods of hydraulic flow. Good look with your work!
Too good..How nicely the Galerkin method is explained without citing any intricate mathematical expressions. Waiting for some more lectures on these FEA topics.
I have two questions about the Galerkin method: 1. What is the reason for forcing the integral of the "weighting function" x "R" to zero such that it yields an optimisation of the residue R in the domain? 2. Why is the chosen weighting function the "same" form? Does it relate to the derivative of the trial function w.r.t. the coefficient, say "A" in this video?
Hello. I have a specific problem in which I have to compute the integral of the residual, R, along the entire length of a beam example. I was wondering if you could walk me through it and answer any questions I have. I would be willing to compensate accordingly. Thanks
I understand intuitively why you do the integral of the residual to be zero… you are summing all of the residuals in the domain and making it zero. Now, when you multiply it by the weighing function, I just don’t understand how it will improve the accuracy of the function representing the approximate solution.
Thanks for the video, its very helpful. Could you also show how to solve the elasticity problem with 2 or 3 quadratic elements and shape functions as weight functions?
Thank you for your video! This really helped me understand the method :) Can you please explain why we need phi and why we should assume phi has the form of the solution? It seems intuitive to me that all we need to solve for is \int R dx = 0 instead.
