Second-Order Convergence of the Linearly Extrapolated Crank–Nicolson Method for the Navier–Stokes Equations with H1 Initial Data

Buyang Li; Shu Ma; Na Wang

doi:10.1007/s10915-021-01588-8

Second-Order Convergence of the Linearly Extrapolated Crank–Nicolson Method for the Navier–Stokes Equations with H¹ Initial Data

Buyang Li
, Shu Ma
, Na Wang

Research output: Journal article publication › Journal article › Academic research › peer-review

18 Citations (Scopus)

Abstract

This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with H¹ initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.

Original language	English
Article number	70
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Scientific Computing
Volume	88
Issue number	3
DOIs	https://doi.org/10.1007/s10915-021-01588-8
Publication status	Published - Sept 2021

Keywords

Error estimate
Linearly extrapolated Crank–Nicolson method
Locally refined stepsizes
Navier–Stokes equations
Nonsmooth initial data

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

More information

10.1007/s10915-021-01588-8

http://hdl.handle.net/10397/93848

Cite this

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title = "Second-Order Convergence of the Linearly Extrapolated Crank–Nicolson Method for the Navier–Stokes Equations with H1 Initial Data",

abstract = "This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with H1 initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.",

keywords = "Error estimate, Linearly extrapolated Crank–Nicolson method, Locally refined stepsizes, Navier–Stokes equations, Nonsmooth initial data",

author = "Buyang Li and Shu Ma and Na Wang",

note = "Funding Information: The research of Buyang Li and Shu Ma were partially funded by the internal grant ZZKQ at The Hong Kong Polytechnic University. The research of Na Wang was partially funded by the National Natural Science Foundation of China (NSFC Grant U1930402). Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Li, Buyang

AU - Ma, Shu

AU - Wang, Na

N1 - Funding Information: The research of Buyang Li and Shu Ma were partially funded by the internal grant ZZKQ at The Hong Kong Polytechnic University. The research of Na Wang was partially funded by the National Natural Science Foundation of China (NSFC Grant U1930402). Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

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N2 - This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with H1 initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.

AB - This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with H1 initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.

KW - Error estimate

KW - Linearly extrapolated Crank–Nicolson method

KW - Locally refined stepsizes

KW - Navier–Stokes equations

KW - Nonsmooth initial data

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DO - 10.1007/s10915-021-01588-8

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