The Prager-Synge theorem in reconstruction based a posteriori error estimation

Fleurianne Bertrand; Daniele Boffi

doi:10.1090/conm/754

The Prager-Synge theorem in reconstruction based a posteriori error estimation

Fleurianne Bertrand, Daniele Boffi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Professional

Abstract

In this paper we review the hypercircle method of Prager and Synge. This theory inspired several studies and induced an active research in the area of a posteriori error analysis. In particular, we review the Braess-Schöberl error estimator in the context of the Poisson problem. We discuss adaptive finite element schemes based on two variants of the estimator and we prove the convergence and optimality of the resulting algorithms.

Original language	English
Title of host publication	75 Years of Mathematics of Computation
Subtitle of host publication	Symposium Celebrating 75 Years of Mathematics of Computation November 1–3, 2018
Editors	Susanne C. Brenner, Igor Shparlinski, Chi-Wang Shu, Daniel B. Szyld
Place of Publication	Providence, RI
Publisher	American Mathematical Society
Number of pages	20
ISBN (Electronic)	978-1-4704-5637-5
ISBN (Print)	978-1-4704-5163-9
DOIs	https://doi.org/10.1090/conm/754
Publication status	Published - 2020
Externally published	Yes
Event	Celebrating 75 Years of Mathematics of Computation 2018 - Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, United States Duration: 1 Nov 2018 → 3 Nov 2018

Publication series

Name	Contemporary Mathematics
Publisher	American Mathematical Society
Volume	754
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Conference

Conference	Celebrating 75 Years of Mathematics of Computation 2018
Country/Territory	United States
City	Providence
Period	1/11/18 → 3/11/18

Keywords

math.NA
cs.NA
n/a OA procedure

Access to Document

10.1090/conm/754

1 Working paper

The Prager-Synge theorem in reconstruction based a posteriori error estimation
Bertrand, F. & Boffi, D., 2019, ArXiv.org, 20 p.
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Bertrand, F., & Boffi, D. (2020). The Prager-Synge theorem in reconstruction based a posteriori error estimation. In S. C. Brenner, I. Shparlinski, C.-W. Shu, & D. B. Szyld (Eds.), 75 Years of Mathematics of Computation: Symposium Celebrating 75 Years of Mathematics of Computation November 1–3, 2018 (Contemporary Mathematics; Vol. 754). American Mathematical Society. https://doi.org/10.1090/conm/754

Bertrand, Fleurianne ; Boffi, Daniele. / The Prager-Synge theorem in reconstruction based a posteriori error estimation. 75 Years of Mathematics of Computation: Symposium Celebrating 75 Years of Mathematics of Computation November 1–3, 2018. editor / Susanne C. Brenner ; Igor Shparlinski ; Chi-Wang Shu ; Daniel B. Szyld. Providence, RI : American Mathematical Society, 2020. (Contemporary Mathematics).

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abstract = "In this paper we review the hypercircle method of Prager and Synge. This theory inspired several studies and induced an active research in the area of a posteriori error analysis. In particular, we review the Braess-Sch{\"o}berl error estimator in the context of the Poisson problem. We discuss adaptive finite element schemes based on two variants of the estimator and we prove the convergence and optimality of the resulting algorithms. ",

keywords = "math.NA, cs.NA, n/a OA procedure",

author = "Fleurianne Bertrand and Daniele Boffi",

year = "2020",

doi = "10.1090/conm/754",

language = "English",

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series = "Contemporary Mathematics",

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booktitle = "75 Years of Mathematics of Computation",

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note = "Celebrating 75 Years of Mathematics of Computation 2018 ; Conference date: 01-11-2018 Through 03-11-2018",

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Bertrand, F & Boffi, D 2020, The Prager-Synge theorem in reconstruction based a posteriori error estimation. in SC Brenner, I Shparlinski, C-W Shu & DB Szyld (eds), 75 Years of Mathematics of Computation: Symposium Celebrating 75 Years of Mathematics of Computation November 1–3, 2018. Contemporary Mathematics, vol. 754, American Mathematical Society, Providence, RI, Celebrating 75 Years of Mathematics of Computation 2018, Providence, Rhode Island, United States, 1/11/18. https://doi.org/10.1090/conm/754

The Prager-Synge theorem in reconstruction based a posteriori error estimation. / Bertrand, Fleurianne; Boffi, Daniele.
75 Years of Mathematics of Computation: Symposium Celebrating 75 Years of Mathematics of Computation November 1–3, 2018. ed. / Susanne C. Brenner; Igor Shparlinski; Chi-Wang Shu; Daniel B. Szyld. Providence, RI: American Mathematical Society, 2020. (Contemporary Mathematics; Vol. 754).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Professional

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AB - In this paper we review the hypercircle method of Prager and Synge. This theory inspired several studies and induced an active research in the area of a posteriori error analysis. In particular, we review the Braess-Schöberl error estimator in the context of the Poisson problem. We discuss adaptive finite element schemes based on two variants of the estimator and we prove the convergence and optimality of the resulting algorithms.

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KW - cs.NA

KW - n/a OA procedure

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Bertrand F, Boffi D. The Prager-Synge theorem in reconstruction based a posteriori error estimation. In Brenner SC, Shparlinski I, Shu CW, Szyld DB, editors, 75 Years of Mathematics of Computation: Symposium Celebrating 75 Years of Mathematics of Computation November 1–3, 2018. Providence, RI: American Mathematical Society. 2020. (Contemporary Mathematics). doi: 10.1090/conm/754

The Prager-Synge theorem in reconstruction based a posteriori error estimation

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The Prager-Synge theorem in reconstruction based a posteriori error estimation

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