On Mar 17, 2013, at 5:51 PM, Roy Stogner <[email protected]> wrote:
>>
>> What polynomial is used to create the hierarchic basis?
>
> Hopefully Ben or John will chime in on this one. In 1D the
> p-hierarchic property is enough to determine the basis up to scaling,
> but in 2D and 3D it gets more complicated, and even in 1D I don't know
> how the scaling was chosen.
svn log is not much help here, which goes all the way back to r3, nor is my
memory.
All I have to offer are the cryptic comments int the code:
// All even-terms have the same form.
// (xi^p - 1.)/p!
case 2:
returnval = (xi*xi - 1.)/2.;
break;
case 4:
returnval = (pow<4>(xi) - 1.)/24.;
break;
case 6:
returnval = (pow<6>(xi) - 1.)/720.;
break;
// All odd-terms have the same form.
// (xi^p - xi)/p!
case 3:
returnval = (xi*xi*xi - xi)/6.;
break;
…
Which I'm sorry aren't very helpful.
In 2D and 3D they are extended as a tensor product for quads and hexes, have
their own flavor on triangles, and do not appear to be implemented for tets.
-Ben
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