Constructions of some minimal finite element systems

Snorre H. Christiansen; Andrew Gillette

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arXiv · 1504.04670

Constructions of some minimal finite element systems

Snorre H. Christiansen·Andrew Gillette

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Abstract

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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Snorre H. Christiansen, Andrew Gillette. 2015-04-18. Constructions of some minimal finite element systems. https://arxiv.org/abs/1504.04670

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