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)?


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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...


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