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Calcolo
Erschienen in: Calcolo 1/2023

01.03.2023

Gradient recovery based a posteriori error estimator for the adaptive direct discontinuous Galerkin method

verfasst von: Huihui Cao, Yunqing Huang, Nianyu Yi

Erschienen in: Calcolo | Ausgabe 1/2023

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Abstract

In this paper, we propose a gradient recovery method for the direct discontinuous Galerkin (DDG) method. A quadratic polynomial is obtain by using the local discrete least-squares fitting to the gradient of numerical solution at certain sampling points. The recovered gradient is defined on a piecewise continuous space, and it may be discontinuous on the whole domain. Based on the recovered gradient, we introduce a posteriori error estimator which takes the \(L^2\) norm of the difference between the direct and post-processed approximations. Some benchmark test problems with typical difficulties are carried out to illustrate the superconvergence of the recovered gradient and validate the asymptotic exactness of the recovery-based a posteriori error estimator. Most of the test problems are from the US National Institute for Standards and Technology (NIST).
Vorheriger Artikel Spectral methods in space and time for parabolic problems on semi-infinite domains
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Metadaten
Titel
Gradient recovery based a posteriori error estimator for the adaptive direct discontinuous Galerkin method
verfasst von
Huihui Cao
Yunqing Huang
Nianyu Yi
Publikationsdatum
01.03.2023
Verlag
Springer International Publishing
Erschienen in
Calcolo / Ausgabe 1/2023
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-023-00513-9

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