Hello, thank you for the comment. You are probably referring to the coercivity part. The function u is in H1 which means that the norm and its gradient are bounded. The bilinear form is greater than constant times the L2 norm squared. This comes from employing poincare inequality in reverse way. Poincare inequality associates the u in L2 with gradient in L2.
@@alexandroskyriakis3675 Thank you for your answer. Maybe i am understanding things incorrectly, but the bilinear form B: X x X --> R is with the Hilbert space X = H1, right? Doesn't that mean that in showing coercivity we have to use the H1-norm? Sorry if i am mistaken (edit: it wouldnt be a problem to show it for the H1-norm because of your nice work and the fact that ||u||_L2
Your remarks are absolutely spot on. I have used H1 norms for continuity. I will reupload the video using H1 norm for the coercivity part. This will make things more consistent.
nice video man, but why do we take u in the L2-norm and not in H1-norm? (I thougth u is element of H1)
Hello, thank you for the comment. You are probably referring to the coercivity part. The function u is in H1 which means that the norm and its gradient are bounded. The bilinear form is greater than constant times the L2 norm squared. This comes from employing poincare inequality in reverse way. Poincare inequality associates the u in L2 with gradient in L2.
@@alexandroskyriakis3675 Thank you for your answer. Maybe i am understanding things incorrectly, but the bilinear form B: X x X --> R is with the Hilbert space X = H1, right? Doesn't that mean that in showing coercivity we have to use the H1-norm? Sorry if i am mistaken (edit: it wouldnt be a problem to show it for the H1-norm because of your nice work and the fact that ||u||_L2
Your remarks are absolutely spot on. I have used H1 norms for continuity. I will reupload the video using H1 norm for the coercivity part. This will make things more consistent.
@@alexandroskyriakis3675 thanks for your fast and kind replies, keep up your good work!
@@speckpackgamer I have reuploaded the video using H1 norms for boundedness and coercivity of the bilinear form.