Re: [Libmesh-users] 1D/2D elements in 3D space

[Roy S. <roy...@ic...>]

On Mon, 12 Feb 2018, Manav Bhatia wrote:

> So, would the shape function derivatives account the orientation of the element?
>
> For instance, a 1D element oriented along:   x-axis   vs   y-axis   vs   x=y line.
>
> In all cases, there is only one shape function defined along the
> element coordinate. But its derivative wrt x and y will vary. Is
> this handled for both 1st order and 2nd order Lagrange (for
> instance)?

IIRC it's handled properly for all scalar-valued elements, where by
"properly" I mean that the derivative is returned as a directional
gradient in LIBMESH_DIM-dimensional space.  E.g. If you have an EDGE2
element with a value of 1 at the origin and 0 at the other end, then
if the other end is at (x,y,z) the gradient in physical space we
return should be (-x, -y, -z).

That means that if you're solving e.g. a Laplacian problem, then you
want to be integrating grad(u)*grad(v) as a dot product of 2 vectors,
not just assuming that you can still ignore the m>>n indexed
components for an n-dimensional element.

I'm actually not sure if anybody ever made sure we support embedded
vector-valued elements.  Cc'ing Paul Bauman; if he didn't do it then
nobody did.
---
Roy