Contraction property of adaptive hybridizable discontinuous galerkin methods

Bernardo Cockburn; Ricardo H. Nochetto; Wujun Zhang

doi:10.1090/mcom/3014

Contraction property of adaptive hybridizable discontinuous galerkin methods

Bernardo Cockburn, Ricardo H. Nochetto, Wujun Zhang

Mathematics

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

10 Scopus citations

Abstract

We establish the contraction property between consecutive loops of adaptive hybridizable discontinuous Galerkin methods for the Poisson problem with homogeneous Dirichlet condition. The contractive quantity is the sum of the square of the L²-norm of the flux error, which is not even monotone, and a two-parameter scaled error estimator, which quantifies both the lack of H(div, Ω)-conformity and the deviation from a gradient of the approximate flux. A distinctive and novel feature of this analysis, which enables comparison between two nested meshes, is the lifting of trace residuals from inter-element boundaries to element interiors.

Original language	English (US)
Pages (from-to)	1113-1141
Number of pages	29
Journal	Mathematics of Computation
Volume	85
Issue number	299
DOIs	https://doi.org/10.1090/mcom/3014
State	Published - 2016

Bibliographical note

Funding Information:
The first author was partially supported by NSF Grant DMS-1115331 and by the Minnesota Supercomputing Institute. The second author was partially supported by NSF Grant DMS-1109325. The third author was partially supported by NSF Grants DMS-1115331 and DMS-1109325.

Publisher Copyright:
© 2015 American Mathematical Society.

Access

10.1090/mcom/3014

OpenUrl availability

Full text

Cite this

@article{508b4fe7e42e4267ac46eb75fe1f5f3d,

title = "Contraction property of adaptive hybridizable discontinuous galerkin methods",

abstract = "We establish the contraction property between consecutive loops of adaptive hybridizable discontinuous Galerkin methods for the Poisson problem with homogeneous Dirichlet condition. The contractive quantity is the sum of the square of the L2-norm of the flux error, which is not even monotone, and a two-parameter scaled error estimator, which quantifies both the lack of H(div, Ω)-conformity and the deviation from a gradient of the approximate flux. A distinctive and novel feature of this analysis, which enables comparison between two nested meshes, is the lifting of trace residuals from inter-element boundaries to element interiors.",

author = "Bernardo Cockburn and Nochetto, {Ricardo H.} and Wujun Zhang",

note = "Funding Information: The first author was partially supported by NSF Grant DMS-1115331 and by the Minnesota Supercomputing Institute. The second author was partially supported by NSF Grant DMS-1109325. The third author was partially supported by NSF Grants DMS-1115331 and DMS-1109325. Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2016",

doi = "10.1090/mcom/3014",

language = "English (US)",

volume = "85",

pages = "1113--1141",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

number = "299",

}

TY - JOUR

T1 - Contraction property of adaptive hybridizable discontinuous galerkin methods

AU - Cockburn, Bernardo

AU - Nochetto, Ricardo H.

AU - Zhang, Wujun

N1 - Funding Information: The first author was partially supported by NSF Grant DMS-1115331 and by the Minnesota Supercomputing Institute. The second author was partially supported by NSF Grant DMS-1109325. The third author was partially supported by NSF Grants DMS-1115331 and DMS-1109325. Publisher Copyright: © 2015 American Mathematical Society.

PY - 2016

Y1 - 2016

N2 - We establish the contraction property between consecutive loops of adaptive hybridizable discontinuous Galerkin methods for the Poisson problem with homogeneous Dirichlet condition. The contractive quantity is the sum of the square of the L2-norm of the flux error, which is not even monotone, and a two-parameter scaled error estimator, which quantifies both the lack of H(div, Ω)-conformity and the deviation from a gradient of the approximate flux. A distinctive and novel feature of this analysis, which enables comparison between two nested meshes, is the lifting of trace residuals from inter-element boundaries to element interiors.

AB - We establish the contraction property between consecutive loops of adaptive hybridizable discontinuous Galerkin methods for the Poisson problem with homogeneous Dirichlet condition. The contractive quantity is the sum of the square of the L2-norm of the flux error, which is not even monotone, and a two-parameter scaled error estimator, which quantifies both the lack of H(div, Ω)-conformity and the deviation from a gradient of the approximate flux. A distinctive and novel feature of this analysis, which enables comparison between two nested meshes, is the lifting of trace residuals from inter-element boundaries to element interiors.

UR - http://www.scopus.com/inward/record.url?scp=84959455409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959455409&partnerID=8YFLogxK

U2 - 10.1090/mcom/3014

DO - 10.1090/mcom/3014

M3 - Article

AN - SCOPUS:84959455409

SN - 0025-5718

VL - 85

SP - 1113

EP - 1141

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 299

ER -

Contraction property of adaptive hybridizable discontinuous galerkin methods

Abstract

Bibliographical note

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this