Dear Martin, Many thanks for your reply. I've realized that indeed mixed elements have been widely used for phase-field equation. It's very helpful, and I appreciate it!
Best, Jinhyun On Thursday, October 6, 2016 at 4:16:41 PM UTC-4, Martin Kronbichler wrote: > > Dear Jinhyun, > > deal.II does not support C1-elements (at least not on general meshes and > in 3D). However, the standard way of dealing with such problems is to > rewrite the phase field equation as a system of two equations, each of > which only has up to second derivatives. In terms of the phase field model, > you typically use a concentration as the primary variable and the chemical > potential (defined as the Laplacian of the concentration plus some > potential in C, e.g. double well) as a secondary variable. There is plenty > of finite element literature on this approach, including one of my own > papers > http://www.sciencedirect.com/science/article/pii/S0898122112004191 > (equation (2)) ;-) > > Best, > Martin > > On Saturday, October 1, 2016 at 12:02:09 AM UTC+2, Jinhyun wrote: >> >> Hello All, >> >> I'm interested in solving a PDE involving a 4th order derivative >> (specifically, the 4th order phase-field model proposed by Borden et al. >> 2014). >> <http://www.sciencedirect.com/science/article/pii/S0045782514000292>I >> believe such equations require C1 continuous elements but this is >> challenging due to lower order of continuity at element boundaries. It >> seems that this issue has been discussed in a previous thread >> <https://groups.google.com/forum/#!topic/dealii/y-Jnn4uuSsY> and deal.II >> yet supported such elements. >> >> I just wonder if this is still the case. Using isogeometric elements >> appear a good way to resolve this issue, and I think there has been recent >> progress in supporting isogeometric analysis in deal.II. I'm novice in this >> aspect though, and would greatly appreciate any advice on this matter. My >> goal is to extend the current solver for the 2nd-order phase-field model to >> the 4th-order one, with minimal efforts. >> >> Thanks very much! >> Jinhyun >> > -- 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.
