[petsc-users] DMPlex higher order elements

[Andrew Ho]

Good geometric accuracy is very import for achieving appropriate
convergence rates in complex geometry, not just using higher order
polynomials on flat elements.

If you look at Hesthaven's book Nodal Discontinuous Galerkin Methods, Table
9.1 shows that without support for curved elements, higher order DG element
on flat elements converges at sub optimal rates due to inaccuracies
produced by the boundary conditions.

There's no way to re-construct this curved information correctly after the
fact; it must be generated by the meshing software.

On Wed, Aug 24, 2016 at 10:12 AM, Jed Brown <jed at jedbrown.org> wrote:

> Matthew Knepley <knepley at gmail.com> writes:
> >> Yes, I do not support that since I think its a crazy way to talk about
> >> things. All the topological information is in the Tri3 mesh, and
> >> Cubit has no business telling me about the function space.
> >>
> >>
> >> Do you support / plan to support curved elements?
> >>
> >
> > I had "support" in there, but there were bugs. Toby and Mark discovered
> > these, and Toby has fixed them. I think
> > all of the fixes are in master now.
>
> The context is clearly that the mesh generator needs to express the
> curved elements.  DMPlex doesn't have a geometric model available, so it
> doesn't know how to make the Tri3 elements curve to conform more
> accurately to the boundary.  The mesh generator has no business telling
> you what function space to use for your solution, but it'd be a shame to
> prevent it from expressing element geometry.
>



-- 
Andrew Ho
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