Quoting Ronan Perrussel <[EMAIL PROTECTED]>: >> >> Ok, after checking the implementation of Nedelec elements in >> Getfem++, I see that there may be a difference with the common >> definition of these elements. >> In order to have a general implementation (for curved elements for >> instance) and a maximum of computation done only once, they are >> defined via a reference element. >> What seems to be litigious is that that the base functions are >> transported via the geometric transformation like vectors. That is, >> they are multiplied to the left by the gradient of the >> transformation. I tried to change this and transport them like >> gradients (i.e. multiplied by the transposed inverse of the >> gradient of the transformation) and I have the same results as >> your python program. >> It is a little bit annoying because this implies that there is two >> kind of intrinsic vectorial elements, those which are transported >> as vector and thos which are transported as gradients. >> >> My question is : Is there a big difference in the capability of >> approximation between the two versions ? The one which is presently >> implemented in getfem is nevertheless a a valid finite element >> (not really the Nedelec one). Should I give two versions ? >> I am not a so much specialist in Nedelec elements, so I would >> appreciate your advice. >> >> >> > Dear Yves, > > in fact (limited to my personal use) there are two kinds of intrisic > vectorial elements : the H(rot) conformal and the H(div) conformal > elements. > > If the usual definition of the Nedelec element is kept on the reference > element but the transformation used is not the valid one, the obtained > finite element family should not be H(curl) conformal. > > My advice is then to keep only the original Nedelec family. > > Best regards, > Ronan
Dear Ronan, You are of course perfectly right. The property to be conserved by the geometric transformation is to be H(rot) conformal for the Nedelec elements and H(div) conformal for the Raviart-Thomas ones. I checked that it corresponds to transform the base function as gradients for the H(rot) conformal elements and as standard vectors for H(div) conformal ones. So, there is indeed the need of two classes of intrinsic vectorial elements. I added this to the definition of finite elements in Getfem. The Nedelec elements corresponds now to the original definition. Best regards, Yves. _______________________________________________ Getfem-users mailing list [email protected] https://mail.gna.org/listinfo/getfem-users
