Re: [Libmesh-users] hp selection strategy

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

On Thu, 5 Dec 2013, Manav Bhatia wrote:

>    From you definition of *hierarchich*, SZABAB would classify as one, correct? The polynomials are nest.

Bearing in mind that I'm really looking at those elements for the
first time...

The 1D SzaBab elements definitely qualify as nested.  The magic
numbers in those coefficients annoy me... but it looks like they're
all just scaling factors so at least the double-precision wouldn't
kill their convergence rates when compiling with quad-precision.

The 2D SzaBab quads appear to be nested.  So are at least the cubic or
so triangles, so I'd strongly bet the triangles are nested too.

It looks like 3D SzaBab hexes would be easy to define; wonder why
nobody's gotten around to it yet.

>    My experience with HIERARCHIC has been unfavorable, with
> convergence issues of iterative solvers. I have not seen any such
> problems with SZABAB, and BERNSTEIN, so am favoring those.

Strange.  From a brief glance at SZABAB it looked like they were
practically just HIERARCHIC with different scaling factors, the kind
of thing even Jacobi preconditioning would fix.

>    I managed to get the higher order SZABAB working with three modifications:
>  
> --   modified FEInterface::extra_hanging_dofs() to be true for SZABAB.
>  
> --   FEInterface::compute_constraints() does not do anything for SZABAB. Added a case SZABAB: for that.
>  
> --  fe_szabab.C needs FE<2, SZABAB>::compute_constraints.
>  
>    With this, h-refinement of higher order SZABAB works without problems.

Great!  Send us a PR?

> I am not sure if this is the issue plaguing hp-refinement, but I
> will get to it soon.

No, sadly you ran into another bug on the way to the hp bug.
---
Roy