Raviart-Thomas on unit interval

dolfinx
,
1

Hi all,

I was obtaining numerical solutions using RT elements on a 2D mesh, but I realized the problem could be simplified to 1D. However, with the following MWE,

from dolfinx.mesh import create_unit_interval, create_unit_square
from mpi4py import MPI
from dolfinx.fem import functionspace

domain = create_unit_interval(MPI.COMM_WORLD, 10)
# domain = create_unit_square(MPI.COMM_WORLD, 10, 10)  # works
H = functionspace(domain, ("Raviart-Thomas", 1))

I get the error
ValueError: Unknown element family: Raviart-Thomas with cell type interval

Is this because it hasn’t been implemented yet? Or, is there something going on with RT elements in 1D that I don’t understand?

Thank you!
Rob

2

I am not sure what the definition of a RT space on an interval should be. It is not covered in: Raviart–Thomas | DefElement
and as indicated by: https://scicomp.stackexchange.com/questions/31154/mixed-formulation-in-1d a Lagrange space should suffice, as you require continuity across the boundaries.

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