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BIT Numerical Mathematics
Erschienen in: BIT Numerical Mathematics 2/2020

11.09.2019

Nonstandard finite element de Rham complexes on cubical meshes

verfasst von: Andrew Gillette, Kaibo Hu, Shuo Zhang

Erschienen in: BIT Numerical Mathematics | Ausgabe 2/2020

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Abstract

Two general operations are proposed on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of “nonstandard” convergent methods. The first operation, called DoF-transfer, moves edge degrees of freedom to vertices in a way that reduces global degrees of freedom while increasing continuity order at vertices. The second operation, called serendipity, eliminates interior bubble functions and degrees of freedom locally on each element without affecting edge degrees of freedom. These operations can be used independently or in tandem to create nonstandard complexes that incorporate Hermite, Adini and “trimmed-Adini” elements. The resulting elements lead to convergent non-conforming methods for problems requiring stronger regularity and satisfy a discrete Korn inequality. Potential benefits of applying these elements to Stokes, biharmonic and elasticity problems are discussed.
Vorheriger Artikel Poincaré–Friedrichs inequalities of complexes of discrete distributional differential forms
Nächster Artikel Convergence analysis of a finite difference scheme for a two-point boundary value problem with a Riemann–Liouville–Caputo fractional derivative

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Metadaten
Titel
Nonstandard finite element de Rham complexes on cubical meshes
verfasst von
Andrew Gillette
Kaibo Hu
Shuo Zhang
Publikationsdatum
11.09.2019
Verlag
Springer Netherlands
Erschienen in
BIT Numerical Mathematics / Ausgabe 2/2020
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-019-00779-y

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