其中为定义域内所有节点的集合;与是传统有限元中的形函数,他们大部分情况下会相等(这里区别表示是由于,在后期一些高阶广义有限元的发展中,一些研究者曾尝试在这两项中使用不同阶数的形函数);系数是标准有限元的节点所对应的自由度(degrees of freedom);是强化项引入的额外节点自由度,对应强化项作用的强化节点(enriched nodes),即是包含非连续的单元网格的节点。
作为该公式中最重要的部分,是结合对解当中非连续性的预了解而建立的强化函数(enrichment function)。与的乘积,即运用了传统有限元拉格朗日形函数的单位分解性质(partition of unity property):
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