Re: [Libmesh-users] Finite element types

[Hubert W. <hub...@gm...>]

On 30.10.2018 16:50, John Peterson wrote:
>
>
> On Tue, Oct 30, 2018 at 9:28 AM Hubert Weissmann 
> <hub...@gm... <mailto:hub...@gm...>> wrote:
>
>     Dear all,
>
>     I have trouble with the regularity of my solution (using
>     Lagrange-elements, only continuity is ensured), and therefore
>     thinking
>     whether I should switch to Clough-Tocher elements or Hermite elements.
>
>
> Are you solving a problem (e.g. biharmonic equation) where you expect 
> the solution to be in C^1?
>
I forgot to mention: I am solving the laplace equation.
In principle I expect my solution to be at least in C^2; so any 
improvement of the continuity is appreciated.

> Usually using more complicated elements doesn't buy you much unless 
> the regularity of the problem calls for it, but that's just my 
> personal experience...
In principle, I agree with you; in the FE-region, it looks quite fine 
with Lagrange elements. But since the boundary to infinite elements is 
really bad, I hope to improve with other elements.
The main disadvantage is that none of them are implemented for infinite 
elements nor for Tets, which I use since they are much easier to setup; 
but I might change this...

>
>
>     But there seems to be only very little literature, where element
>     types
>     are discussed in more detail...
>
>     Can probably someone point me to some books/articles which are
>     helpful
>     in this respect?
>
>
> I'd say Roy's thesis would be a good place to start:
>
> https://repositories.lib.utexas.edu/handle/2152/17797
Thanks for that hint: It looks quite interesting; I'll have a closer look.
>
> -- 
> John

Hubert