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

Fleurianne Bertrand; Daniele Boffi

doi:10.1090/conm/754/15152

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

Fleurianne Bertrand, Daniele Boffi

King Abdullah University of Science and Technology

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

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–Schoberl 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 (US)
Title of host publication	75 Years of Mathematics of Computation
Publisher	American Mathematical Society
Pages	45-67
Number of pages	23
ISBN (Print)	9781470451639
DOIs	https://doi.org/10.1090/conm/754/15152
State	Published - Jul 30 2020

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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–Schoberl 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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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–Schoberl 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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The Prager–Synge theorem in reconstruction based a posteriori error estimation

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