On Tue, Jun 17, 2008 at 4:16 PM, John Peterson <[EMAIL PROTECTED]> wrote:
> On Tue, Jun 17, 2008 at 4:02 PM, Roy Stogner <[EMAIL PROTECTED]> wrote:
>>
>> On Tue, 17 Jun 2008, John Peterson wrote:
>>
>>> On Tue, Jun 17, 2008 at 2:11 PM, Benjamin Kirk <[EMAIL PROTECTED]>
>>> wrote:
>>>
>>>> Do any of you have access to "The finite element method" vol. 1 by
>>>> Zienkiewicz & Taylor? Pg. 222 is referenced as the source for orders
>>>> 1-5,
>>>> and I want to make sure that the 5th-order rule has only 15 points...
>>>
>>> I found one of Zienkiewicz's books on google books
>>>
>>> The Finite Element Method: Its Basis and Fundamentals
>>>
>>> Redacted from the book preview is pg. 167, which should contain Table
>>> 5.4 -- tetrahedral quadrature formulae... this always seems to happen
>>> to me with Google Books.
>>>
>>> Maybe Roy can send Vikram to get one of the many copies from the UT
>>> Engineering Library: TA 640.2 Z5
>>
>> No luck; at least in the editions on the shelves (3rd through 6th),
>> the quadrature for tets only runs up through 3rd-order.
>
> Crappy... I guess the comment in the code only applied to the rules up
> to that order. I'll search around a bit. I actually have a Gaussian
> quadrature textbook at home, so I'll look there too.
Well, that (Stroud's quadrature book) was a bust. It really only has
one-dimensional quadrature rules for integrals with non-standard
weighting functions.
I'm not sure when I'll next be on campus, and this article is too old
to be available online yet, but if somebody wants to take a look, it
should have tet rules up to at least 8th order. And a warning, the
eighth-order rule's centroid weighting apparently has the wrong sign.
@article{17769,
author = {P Keast},
title = {Moderate-degree tetrahedral quadrature formulas},
journal = {Comput. Methods Appl. Mech. Eng.},
volume = {55},
number = {3},
year = {1986},
issn = {0045-7825},
pages = {339--367},
doi = {http://dx.doi.org/10.1016/0045-7825(86)90059-9},
publisher = {Elsevier Sequoia S. A.},
address = {Lausanne, Switzerland, Switzerland},
}
--
John
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