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Journal of Applied Mathematics and Computing

Erschienen in:

02.12.2022 | Original Research

The supercloseness property of the Stoke projection for the transient Navier–Stokes equations and global superconvergence analysis

verfasst von: Minghao Li, Liuchao Xiao, Zhenzhen Li

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 2/2023

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Abstract

In this paper, we derive the supercloseness properties and global superconvergence results for the implicit Euler scheme of the transient Navier–Stokes equations. Using a prior estimate of finite element solutions, the properties of the Stokes projection and Stokes operator, the derivative transforming skill and the \(H^{-1}\)-norm estimate, we deduce the supercloseness properties of the Stokes projection for the velocity in \(L^\infty (H^1)\)-norm and pressure in \(L^\infty (L^2)\)-norm. Then the supercloseness properties of the interpolation operators are obtained for two pairs of rectangular element: the bilinear-constant element and the Bernadi–Raugel element. Finally, by the interpolation postprocessing technique, we obtain the global superconvergent results. Compared with previous results, no time step restriction is required in the analysis, and moreover, the supercloseness analysis is based on the Stokes projection, which makes the proof more concise.

Vorheriger Artikel A modified Levenberg–Marquardt method for solving system of nonlinear equations

Nächster Artikel Control strategies of a stochastic social obesity epidemic model in the region of Valencia, Spain

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Titel: The supercloseness property of the Stoke projection for the transient Navier–Stokes equations and global superconvergence analysis
verfasst von: Minghao Li
Liuchao Xiao
Zhenzhen Li
Publikationsdatum: 02.12.2022
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 2/2023
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-022-01824-w

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