On Tuesday, August 23, 2016 at 12:51:53 PM UTC-4, Wolfgang Bangerth wrote: > > > Thomas, > > > I was able to solve for the vector mean curvature using the weak form of > > the identity k_bar = laplacian_X id_X, where X is a codimension 1 > > manifold without boundary. The image above is a plot of the square of > > the mean curvature on an ellipsoid with semi principle axes a=1,b=2,c=3. > > Great, this looks roughly correct I would say. Have you checked that the > numerical values are correct as well? > > I implemented an exact solution for the mean curvature for ellipsoids (it's a slightly ugly expression, I just took it from here: http://math.stackexchange.com/a/540820), and I computed the L2 and Linfty errors between my computed values and that expression. The result: Convergence wrt mesh refinement - about an order of magnitude decrease in each norm per increment of refine_global(). That's not a tidy way to put it, but it was quick and easy.
> I think this would actually make for a really nice addition to the set > of tutorials, or the code gallery at > http://dealii.org/code-gallery.html > Would you be interested in getting it there? (Maybe after rewriting it > in such a way that you solve for all three components at once?) > > Yes, I am very interested in doing this ( but it will have to wait until September), thank you for asking. -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
