Re: [Libmesh-devel] Higher than second order elements.

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

On Mon, 2 Mar 2009, Ondrej Certik wrote:

> That's awesome that you are interested in this. At this moment, I am
> quite busy with other things, but I am very interested in this
> comparison. Does the isotropic hp-adaptivity work in 3d?

It works for any elements we've got hierarchic basis functions
available on, but right now that means just hexes in 3D.

> <ben...@na...> wrote:
>> is that these tend to be more "industrial-type" applications, where
>> higher-order elements are often not used for various reasons (non-smooth
>> solutions, sharp complex geometry, etc...)
>
> In fact, hp-fem performs the best exactly with solutions that are both
> non-smooth and sharp somewhere (it uses a low polynomial order there)
> and very smooth somewhere else in the domain (it uses a high
> polynomial order there).

Yeah; locally non-smooth solutions should be fine for hp elements.
Complex geometry is a little trickier, unless you've got mechanisms
for curved element sides (libMesh does, but only quadratics) and
proper refinement into exactly specified geometry (libMesh doesn't
unless user code adds it).

But I think Ben left out the biggest reasons why industrial
applications don't get solved with hp: formulation fragility and code
complexity.  Some numerical formulations work fine at low order and
require significant analysis and redesign before achieving optimal
convergence (or even converging at all) at high order.  Most
industrial software is complex, and rearchitecting to get faster and
more accurate solves is deemed (rightly or wrongly) less productive
than making a GUI nicer.
---
Roy