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^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

19 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
Number of pages	20
Journal	Journal of Scientific Computing
Volume	88
Issue number	3
Early online date	30 Jul 2021
DOIs	https://doi.org/10.1007/s10915-021-01588-8
Publication status	Published - Sept 2021

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

User-Defined Keywords

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

Access to Document

10.1007/s10915-021-01588-8

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 = "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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T1 - Second-Order Convergence of the Linearly Extrapolated Crank–Nicolson Method for the Navier–Stokes Equations with H1 Initial Data

AU - Li, Buyang

AU - Ma, Shu

AU - Wang, Na

N1 - 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.

PY - 2021/9

Y1 - 2021/9

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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U2 - 10.1007/s10915-021-01588-8

DO - 10.1007/s10915-021-01588-8

M3 - Journal article

AN - SCOPUS:85111707569

SN - 0885-7474

VL - 88

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

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M1 - 70

ER -