The partition of unity finite element method: Basic theory and applications
The partition of unity finite element method: Basic theory and applications
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DOI：
10.1016/s0045-7825(96)01087-0
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发表时间：
1996-12-15
影响因子：
7.2
通讯作者：
Babuska, I
中科院分区：
文献类型：
--
作者：
Melenk, JM;Babuska, I
介绍了单位分解有限元法的基本思想和数学基础。我们将展示如何使用PUFEM来使用所考虑的微分方程的结构来构建有效和鲁棒的方法。虽然该方法及其理论在n维中是有效的，但对于一维模型问题，将给出详细的和说明性的分析。我们确定了一些类的非标准的问题，可以高度受益于PUFEM的优势，并得出结论，本文与一些公开的问题有关的实施方面的PUFEM。
The paper presents the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM). We will show how the PUFEM can be used to employ the structure of the differential equation under consideration to construct effective and robust methods. Although the method and its theory are valid in n dimensions, a detailed and illustrative analysis win be given for a one-dimensional model problem. We identify some classes of non-standard problems which can profit highly from the advantages of the PUFEM and conclude this paper with some open questions concerning implementational aspects of the PUFEM.