Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

Eric T. Chung; Eun Jae Park; Lina Zhao

doi:10.1007/s10915-017-0575-8

Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

Eric T. Chung, Eun Jae Park, Lina Zhao

Department of Computational Science and Engineering

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

14 Citations (Scopus)

Abstract

In this paper, we present for the first time guaranteed upper bounds for the staggered discontinuous Galerkin method for diffusion problems. Two error estimators are proposed for arbitrary polynomial degrees and provide an upper bound on the energy error of the scalar unknown and L²-error of the flux, respectively. Both error estimators are based on the potential and flux reconstructions. The potential reconstruction is given by a simple averaging operator. The equilibrated flux reconstruction can be found by solving local Neumann problems on elements sharing an edge with a Raviart–Thomas mixed method. Reliability and efficiency of the two a posteriori error estimators are proved. Numerical results are presented to validate the theoretical results.

Original language	English
Pages (from-to)	1079-1101
Number of pages	23
Journal	Journal of Scientific Computing
Volume	75
Issue number	2
DOIs	https://doi.org/10.1007/s10915-017-0575-8
Publication status	Published - 2018 May 1

Bibliographical note

Funding Information:
Eun-Jae Park: This author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358. Eric T. Chung’s research is partially supported by the Hong Kong RGC GRF (Project: 14301314) and the CUHK Direct Grant 2016-17.

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.

All Science Journal Classification (ASJC) codes

Software
Theoretical Computer Science
Numerical Analysis
Engineering(all)
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s10915-017-0575-8

Cite this

@article{922589371dd9449683d4c4eed48e2857,

title = "Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method",

abstract = "In this paper, we present for the first time guaranteed upper bounds for the staggered discontinuous Galerkin method for diffusion problems. Two error estimators are proposed for arbitrary polynomial degrees and provide an upper bound on the energy error of the scalar unknown and L2-error of the flux, respectively. Both error estimators are based on the potential and flux reconstructions. The potential reconstruction is given by a simple averaging operator. The equilibrated flux reconstruction can be found by solving local Neumann problems on elements sharing an edge with a Raviart–Thomas mixed method. Reliability and efficiency of the two a posteriori error estimators are proved. Numerical results are presented to validate the theoretical results.",

author = "Chung, {Eric T.} and Park, {Eun Jae} and Lina Zhao",

note = "Funding Information: Eun-Jae Park: This author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358. Eric T. Chung{\textquoteright}s research is partially supported by the Hong Kong RGC GRF (Project: 14301314) and the CUHK Direct Grant 2016-17. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media, LLC.",

year = "2018",

month = may,

day = "1",

doi = "10.1007/s10915-017-0575-8",

language = "English",

volume = "75",

pages = "1079--1101",

journal = "Journal of Scientific Computing",

issn = "0885-7474",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

AU - Chung, Eric T.

AU - Park, Eun Jae

AU - Zhao, Lina

N1 - Funding Information: Eun-Jae Park: This author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358. Eric T. Chung’s research is partially supported by the Hong Kong RGC GRF (Project: 14301314) and the CUHK Direct Grant 2016-17. Publisher Copyright: © 2017, Springer Science+Business Media, LLC.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - In this paper, we present for the first time guaranteed upper bounds for the staggered discontinuous Galerkin method for diffusion problems. Two error estimators are proposed for arbitrary polynomial degrees and provide an upper bound on the energy error of the scalar unknown and L2-error of the flux, respectively. Both error estimators are based on the potential and flux reconstructions. The potential reconstruction is given by a simple averaging operator. The equilibrated flux reconstruction can be found by solving local Neumann problems on elements sharing an edge with a Raviart–Thomas mixed method. Reliability and efficiency of the two a posteriori error estimators are proved. Numerical results are presented to validate the theoretical results.

AB - In this paper, we present for the first time guaranteed upper bounds for the staggered discontinuous Galerkin method for diffusion problems. Two error estimators are proposed for arbitrary polynomial degrees and provide an upper bound on the energy error of the scalar unknown and L2-error of the flux, respectively. Both error estimators are based on the potential and flux reconstructions. The potential reconstruction is given by a simple averaging operator. The equilibrated flux reconstruction can be found by solving local Neumann problems on elements sharing an edge with a Raviart–Thomas mixed method. Reliability and efficiency of the two a posteriori error estimators are proved. Numerical results are presented to validate the theoretical results.

UR - http://www.scopus.com/inward/record.url?scp=85030872428&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030872428&partnerID=8YFLogxK

U2 - 10.1007/s10915-017-0575-8

DO - 10.1007/s10915-017-0575-8

M3 - Article

AN - SCOPUS:85030872428

SN - 0885-7474

VL - 75

SP - 1079

EP - 1101

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 2

ER -

Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this