Finite element potentials

We present an explicit and efficient way for constructing finite elements with assigned gradient, or curl, or divergence. Some simple notions of homology theory and graph theory applied to the finite element mesh are basic tools for devising the solution algorithms.

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Bibliographic Details
Published in:Applied numerical mathematics 2015-09, Vol.95, p.2-14
Main Authors: Alonso Rodríguez, Ana, Valli, Alberto
Format: Article
Language:English
Subjects:
Curl operator
Divergence operator
Finite elements
First homology group
Grad operator
Graph
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Description
Summary:We present an explicit and efficient way for constructing finite elements with assigned gradient, or curl, or divergence. Some simple notions of homology theory and graph theory applied to the finite element mesh are basic tools for devising the solution algorithms.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2014.05.014