Hi John,
> I think this is actually a 14-point rule in Table 2.1. I didn't see
> it explicitly stated anywhere that it was a 15-point rule, and it
> turns out that
>
> 4*w_1 + 4*w_2 + 6*w_3 = 1/6
>
> where 4 and 6 are the cardinality of the \Xi_1 and \Xi_{11} sets,
> respectively. (Awful notation BTW!)
>
> This is equal to the volume of the Tet4 (=1/d!) so I don't think
> there's a 15th point.
Well that's sorted then, thanks. I assumed based on equation (2.1)
that it would be a 15-point rule because (2.1) gives the fifth order
quadrature rule defined in arbitrary dimension, and that includes the
w_0 term. But they mention that Table 2.1 gives "simplified" versions
of the quadrature rules in 2D or 3D, so I guess the w_0 term drops
out in this simplified form.
> This would also explain why it doesn't match our 15-point rule. I'm
> still skeptical of the accuracy-order claims in any case.
hehe, well the way the paper is written doesn't inspire me with
confidence in their results, so I'd be very interested to hear the
results of the comparisons.
- Dave
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