On Mon, Oct 4, 2010 at 11:16 AM, Vijay S. Mahadevan <[email protected]> wrote:
> John,
>
> If I understand the implementation for edges correctly, for all the
> higher order edges, you split the element in half and create 2
> children of same order with h/2. If this is true, I dont see a problem
> with my numbering scheme or the implementation of the embedding
> matrix. Btw, here's the numbering for the edges that I missed out in
> my previous mail.
>
>  *  EGDE5: o----o----o----o----o
>  *         0    2    3    4    1

Hmm, for EDGE5 I think I'd suggest

o----o----o----o----o
0     3     2    4    1

So that it nests with the EDGE3, and I suppose what you have for EDGE6

o----o----o----o----o----o
0      2    3    4    5    1

is OK, there is no nice way to nest orders 4 and 6.  Unless you allow
non-equispaced nodes on the master element?  I don't think there is
any equispacing assumption required for the interpolation estimates to
hold, but it would probably be at least non-standard and confusing to
have them non-equispaced.

> Once I finish testing the 1-d elements completely, I will move to the
> 2-d elements and implement the embedding and mesh generation
> algorithms which still need some cleaning up. Let me know if you have
> any comments.

Are you planning to use isoparametric elements (element map has same
order as basis functions)?  If you can stick to quadratic elements for
the mappings, I don't *think* you need to add any new embedding
matrices, though I could be wrong about that.

For higher-order elements the embedding matrices will be enormous, not
sure we want to mess with these if we don't have to...

-- 
John

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