SIAM Journal on Scientific Computing, Volume 42, Issue 3, Page A1741-A1764, January 2020.
We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. These preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

中文翻译：

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利用非协调内部罚分和静凝聚的有限元方程组的辅助空间预处理

SIAM科学计算杂志，第42卷，第3期，第A1741-A1764页，2020年1月。
我们修改了众所周知的内部罚分有限元离散化方法，以便可以逐个元素地组装。由于引入了与相邻元素之间的接口关联的其他未知数，这是可能的。所得的双线性形式及其Schur补（简化）形式在许多辅助空间预处理器中用于原始的有限元离散化问题。对这些预处理器进行了精细的分析，并在用高阶元素离散化的模型二阶标量椭圆问题上说明了它们的性能。