On 5/2/19 7:26 PM, Doug wrote:
>
> Based on this, I assume that FEValues, which takes a FiniteElement and a
> Mapping, uses them to evaluate the Jacobian field instead of using a bilinear
> mapping as the documentation of Mapping suggests. So FE_DGP would only be
> able
> to parametrize the cell geometry with the polynomial space {1, x, y} instead
> of {1, x, y, xy}.
No, that's not correct. The *element* may only have 3 basis functions, but the
mapping is still bilinear (with four basis functions). These two aspects are
separate -- in fact, the mapping never knows anything about the element anyway.
What this means is that on cells that are not parallelograms, the *mapped*
basis functions may not be linear. You can probably try this out easily if you
just do a single cell that's not a parallelogram, output a solution vector
with one 1 and the rest all zeros, and use DataOut::build_patches(N) with a
sufficiently large N.
> The documentation of FE_DGP does mention similar to this, but I thought this
> only applied to the solution, not the geometric mapping. I would expect the
> geometric mapping to always use a tensor product basis in order to be able to
> represent any straight-sided quads, especially since deal.II only handles
> quads.
Yes, and it does.
> Since the FEValues seems to evaluate Jacobian based on the provided
> FiniteElement, FE_DGP is basically useless since it can only handle truly
> linear elements.
I don't know if that's true (that it's useless), but it's worth keeping the
Jacobian of the mapping and the Jacobians of the shape functions separate --
they're not the same.
Best
Wolfgang
--
------------------------------------------------------------------------
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups
"deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to dealii+unsubscr...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
