On 11/3/23 15:06, M. Bakry wrote:
- it seems that the Piola transform is implemented for the 'codimension=1'
case (according to the templatization). Could codim=1 RT elements be
implemented by computing the RT on the reference quad then by applying the
corresponding Piola transform ?
Marc -- quite possibly. The implementation of the RT element predates the
codimension-1 functionality by several years, and I suspect that the major
issue is that nobody has taken the time to convert the implementation to
support surfaces.
I will note that unless you have a C^1 manifold description -- for example if
you try to describe a surface by using bilinear quads without using a manifold
description -- then the normal vectors from adjacent cells are not going to
point in the same direction (more precisely, they will be tangential to the
cell, but not to the underlying manifold). In that case, you'll end up with a
non-conforming RT space because the normal component of the finite element
field is not continuous across cell interfaces.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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