Hi Firedrake Team,
My name is Natanael Quintino, nice to meet you. I'm a researcher at
Instituto Superior Tecnico of the Universidade de Lisboa, Portugal, and
finite element is my area of expertise.
I'm using the Python-Fenics module in my research and I could talk to
you about hermite basis and get your help, if you are interested and
available. I'm not using Fenicsx yet, because I began to learn Fenics last
year and had some work to develop a program to solve nonlinear stationary
and evolutive pdes with mixed boundary conditions on 1D, 2D and 3D meshes.
I think that it will be so hard to transcript my code from Fenics to
Fenicsx.
One of these pdes is the Biharmonic Equation, which I wanna use the
Hermite's basis to solve it. But this finite element basis is not supported
in the last Fenics version. Handling this situation, I did edit some Fenics
scripts and put the Hermite's basis to work. After some tests, the program
works correctly and the numerical error converges. To 1D meshes it works,
but to 2D and 3D meshes it doesn't. In my PhD experience, I did verify that
to obtain consistent results using the Hermite's basis in 2D meshes we need
to consider the mixed derivative, *d²u/dxy*, as a dof too. I did try to
edit Fenics code to consider more one dof to each triangle vertex on 2D
domains, for example, but I didn't do it.
After hearing my situation could you help me with any suggestions or
guidance?
I thank you in advance for your attention and time.
Kind regards,
Natanael Quintino