From: David Knezevic <dknez@MIT.EDU>  20090216 16:06:16

The quadrature rules for simplices in libmesh have been recently refurbished I think (thanks John!) and with that in mind I thought I'd just pass on a link to a new paper I saw about this topic: Linbo Zhang, Tao Cui and Hui Liu A Set of Symmetric Quadrature Rules on Triangles and Tetrahedra. J. Comp. Math., 27 (2009), pp. 8996. http://www.globalsci.org/jcm/volumes/v27n1/pdf/27189.pdf It's got a nice description of their algorithm for finding symmetric quadrature rules, and they list a bunch of them. However, happily, their quadrature rules don't offer much of an improvement over the ones already available in libMesh (except that they have explicitly found quadrature rules on tets up to order 14).  Dave 