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Corpus ID: 244908891

Unifying the geometric decompositions of full and trimmed polynomial spaces in finite element exterior calculus

@article{Isaac2021UnifyingTG,
title={Unifying the geometric decompositions of full and trimmed polynomial spaces in finite element exterior calculus},
author={Toby Isaac},
journal={ArXiv},
year={2021},
volume={abs/2112.02174}
}

Arnold, Falk, & Winther, in Finite element exterior calculus, homological techniques, and applications (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of trace-free subspaces and in Geometric decompositions and local bases for finite element differential forms (2009) the same authors give direct constructions of extension operators for the same spaces. The two families – full and trimmed – are treated separately, using… Expand

Finite element exterior calculus is an approach to the design and understanding of finite element discretizations for a wide variety of systems of partial differential equations. This approach brings… Expand

The foundations of a new hierarchical modal basis suitable for high-order (hp) finite element discretizations on unstructured meshes is described, based on a generalized tensor product of mixed-weight Jacobi polynomials.Expand

The problem of constructing hierarchic bases for finite element discretization of the spaces H1, H(curl), H(div) and L2 on tetrahedral elements is addressed. A simple and efficient approach to… Expand

We give a systematic self-contained exposition of how to construct geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a… Expand