This paper considers the structure of basis functions in the bilinear immersed finite element space for two dimensional elliptic interface problems. On a rectangular interface element, each immersed basis function can be decomposed into a standard bilinear basis function and a corresponding bubble function, which provides another perspective on the nature of immersed basis functions. Detailed expressions of these bubble functions are presented on the reference element. The same pattern can be carried out for other immersed finite element spaces in a similar manner.

中文翻译：

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关于椭圆界面问题的浸入式有限元基函数的注记

本文考虑了二维椭圆界面问题在双线性沉浸有限元空间中基函数的结构。在矩形界面元素上，每个浸没基函数都可以分解为标准双线性基函数和相应的气泡函数，这为浸没基函数的性质提供了另一种观点。这些气泡函数的详细表达式在参考元素上给出。可以类似的方式对其他浸入式有限元空间执行相同的模式。