Local L 2-bounded commuting projections in FEEC

Douglas Arnold; Johnny Guzmán

doi:10.1051/m2an/2021054

Local L ²-bounded commuting projections in FEEC

Douglas Arnold, Johnny Guzmán

School of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We construct local projections into canonical finite element spaces that appear in the finite element exterior calculus. These projections are bounded in L2 and commute with the exterior derivative.

Original language	English (US)
Pages (from-to)	2169-2184
Number of pages	16
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	55
Issue number	5
DOIs	https://doi.org/10.1051/m2an/2021054
State	Published - Sep 1 2021

Bibliographical note

Funding Information:
Acknowledgements. The work of the first author was supported by Simons Foundation grant 601937, DNA. The second author was partially supported by NSF grant DMS-1913083.

Publisher Copyright:
© 2021 The authors. Published by EDP Sciences, SMAI.

Keywords

Cochain projection
Commuting projection
Finite element exterior calculus

Publisher link

10.1051/m2an/2021054

Find It

Find It at U of M Libraries

Cite this

@article{1d2fd67cb29b4e06922be039fb0d7734,

title = "Local L 2-bounded commuting projections in FEEC",

abstract = "We construct local projections into canonical finite element spaces that appear in the finite element exterior calculus. These projections are bounded in L2 and commute with the exterior derivative.",

keywords = "Cochain projection, Commuting projection, Finite element exterior calculus",

author = "Douglas Arnold and Johnny Guzm{\'a}n",

note = "Funding Information: Acknowledgements. The work of the first author was supported by Simons Foundation grant 601937, DNA. The second author was partially supported by NSF grant DMS-1913083. Publisher Copyright: {\textcopyright} 2021 The authors. Published by EDP Sciences, SMAI.",

year = "2021",

month = sep,

day = "1",

doi = "10.1051/m2an/2021054",

language = "English (US)",

volume = "55",

pages = "2169--2184",

journal = "Mathematical Modelling and Numerical Analysis",

issn = "0764-583X",

publisher = "EDP Sciences",

number = "5",

}

TY - JOUR

T1 - Local L 2-bounded commuting projections in FEEC

AU - Arnold, Douglas

AU - Guzmán, Johnny

N1 - Funding Information: Acknowledgements. The work of the first author was supported by Simons Foundation grant 601937, DNA. The second author was partially supported by NSF grant DMS-1913083. Publisher Copyright: © 2021 The authors. Published by EDP Sciences, SMAI.

PY - 2021/9/1

Y1 - 2021/9/1

N2 - We construct local projections into canonical finite element spaces that appear in the finite element exterior calculus. These projections are bounded in L2 and commute with the exterior derivative.

AB - We construct local projections into canonical finite element spaces that appear in the finite element exterior calculus. These projections are bounded in L2 and commute with the exterior derivative.

KW - Cochain projection

KW - Commuting projection

KW - Finite element exterior calculus

UR - http://www.scopus.com/inward/record.url?scp=85117285850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85117285850&partnerID=8YFLogxK

U2 - 10.1051/m2an/2021054

DO - 10.1051/m2an/2021054

M3 - Article

AN - SCOPUS:85117285850

VL - 55

SP - 2169

EP - 2184

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

SN - 0764-583X

IS - 5

ER -