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There is at least one quite comprehensive encyclopaedia of quadrature rules that doesn't seem to have been updated in quite a while and has restricted access. This source refers to several classical and modern sources, and generally is well put together. However, it approaches the construction of quadrature rules from the purely theoretical approach and therefore misses out on more practical methods for, say, finite element computation.

Does a more multidisciplinary compendium for quadrature rules exist, or does anyone know of an open-source library that implements a wide swath of such methods for simple domains (such as those used for finite elements)?

Peter Brune
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  • Youe question is a bit open-ended. See faq (http://scicomp.stackexchange.com/faq). – Allan P. Engsig-Karup Jan 06 '12 at 18:42
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    @DavidKetcheson: I think this question is intended to be a community wiki resource because FEM quadrature rules, methodologies, etc. seem to be coming up a lot on SciComp.SE, like http://scicomp.stackexchange.com/q/580/276, http://scicomp.stackexchange.com/q/561/276, http://scicomp.stackexchange.com/q/444/276, and http://scicomp.stackexchange.com/q/287/276. – Geoff Oxberry Jan 06 '12 at 20:01
  • I use midpoint rules for all elements (for higher order elements, I just use corresponding sub-elements). I do not care about dedicated quadrature rules, mostly because I can not find a comprehensive list of them for common elements and do not have time to derive it myself. – Dominik Lark Jan 06 '12 at 19:21

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The libmesh finite element library (libmesh.sf.net) has several families of rules (up to relatively high order) for different finite element types. You might have a look there...

JW Peterson
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