Nice introduction on the Galerkin method. As for the second example(quadratic shape functions), in Matlab code, phi should be modified into "phi=[2*(x-1/2)*(x-1); -4*x*(x-1); 2*x*(x-1/2)]" , the second phi2 has type error. Then, the final coefficients will be [u1 u2 u3]=[0 1/4 1] that is perfectly matching the true function x^2.
Yes, you are right, good catch! I did not simplify that expression in the video, otherwise we would have seen that it is indeed not x^2. The example on the website is accurate however. Thanks for pointing it out!
Nice introduction on the Galerkin method. As for the second example(quadratic shape functions), in Matlab code, phi should be modified into "phi=[2*(x-1/2)*(x-1); -4*x*(x-1); 2*x*(x-1/2)]" , the second phi2 has type error. Then, the final coefficients will be [u1 u2 u3]=[0 1/4 1] that is perfectly matching the true function x^2.
Yes, you are right, good catch! I did not simplify that expression in the video, otherwise we would have seen that it is indeed not x^2. The example on the website is accurate however. Thanks for pointing it out!