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Journal of Scientific Computing

Erschienen in:

01.04.2021

Superconvergent Flux Recovery of the Rannacher–Turek Nonconforming Element

verfasst von: Yuwen Li

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2021

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Abstract

This work presents superconvergence estimates of the nonconforming Rannacher–Turek element for second order elliptic equations on any cubical meshes in \(\mathbb {R}^{2}\) and \(\mathbb {R}^{3}\). In particular, a corrected numerical flux is shown to be superclose to the Raviart–Thomas interpolant of the exact flux. We then design a superconvergent recovery operator based on local weighted averaging. Combining the supercloseness and the recovery operator, we prove that the recovered flux superconverges to the exact flux. As a by-product, we obtain a superconvergent recovery estimate of the Crouzeix–Raviart element method for general elliptic equations.

Vorheriger Artikel A Novel Regularization Based on the Error Function for Sparse Recovery

Nächster Artikel A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions

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Titel: Superconvergent Flux Recovery of the Rannacher–Turek Nonconforming Element
verfasst von: Yuwen Li
Publikationsdatum: 01.04.2021
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-021-01445-8

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