Professor Bangerth - Thank you for your reply. The shape functions of the "quadratic" serendipity elements are very similar to the FE_Q(2) elements except they are derived without any interior nodes (i.e. in 2D the interior node is removed and the shape functions are simple polynomials with 8 undetermined coefficients instead of 9 as with a normal quadratic Lagrange element. Essentially the polynomials are not quadratic complete since they are missing the x^2 * y^2 term). It's pretty simple to express them in 2D and 3D for the "quadratic" case (I put quadratic in quotes since the polynomials are not quadratic complete) but I am more worried about how difficult it would be to get this type of element to work with all of the other functionality in dealii (e.g. the DoFHandler, Triangulation, grid refinement, etc.). Do you have a sense for whether this requires a significant amount of additional effort?
Thank you again, Jonathan On Sunday, August 4, 2019 at 3:58:07 PM UTC-6, Wolfgang Bangerth wrote: > > On 8/3/19 1:17 PM, Jonathan Russ wrote: > > > > How difficult would it be to add serendipity elements to dealii? They > are very > > useful in solid mechanics applications and can greatly reduce the > > computational cost. Is it very difficult to add an element that is the > same is > > FE_Q but without the few extra basis functions when quadratic > polynomials are > > used? i.e. 8-node FE_Q instead of 9-node FE_Q in 2D and 20-node FE_Q > instead > > of 27-node FE_Q in 3D? > > I suspect it's not going to be terribly difficult, but can you explain how > the > shape functions of the serendipity element differ from the ones of > FE_Q(2)? > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > <javascript:> > www: http://www.math.colostate.edu/~bangerth/ > > -- 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. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/3b669c86-d45d-45d4-b06b-8776a6a520e3%40googlegroups.com.
