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arXiv 1504.046702015-04math.NAcs.NA

一些最小有限元系统的构造

Constructions of some minimal finite element systems

University of Oslo（奥斯陆大学）；University of Arizona（亚利桑那大学）

Snorre H. Christiansen, Andrew Gillette

备注：: Various minor changes, based on suggestions of paper referees

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AI总结：

本文探讨了如何构造满足交换插值器和包含指定函数的微分形式空间，并展示了多种已知混合有限元空间如何遵循这一设计原则。

摘要：

在有限元系统框架内，我们展示了如何构造微分形式空间，使其配备交换插值器并包含预设函数，同时在这些约束下保持最小性。我们展示了各种已知的混合有限元空间如何满足这一设计原则，包括修剪多项式微分形式、塞伦迪普ity元素和TNT元素。我们还评论了虚拟元方法，并为包含给定次数多项式的最小兼容有限元系统提供了维度公式。

英文摘要：

Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these constraints. We show how various known mixed finite element spaces fulfill such a design principle, including trimmed polynomial differential forms, serendipity elements and TNT elements. We also comment on virtual element methods and provide a dimension formula for minimal compatible finite element systems containing polynomials of a given degree on hypercubes.

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