A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions

In this article, we first develop a semi-discretized Crank–Nicolson format about time for the two-dimensional non-stationary Stokes equations about vorticity–stream functions and analyze the existence, uniqueness, stability, and convergence of the semi-discretized Crank–Nicolson solutions. Then we e...

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Detalles Bibliográficos
Autores principales: Zhou, Yanjie, Luo, Zhendong, Teng, Fei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6244727/
https://www.ncbi.nlm.nih.gov/pubmed/30839842
http://dx.doi.org/10.1186/s13660-018-1914-5
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author Zhou, Yanjie
Luo, Zhendong
Teng, Fei
author_facet Zhou, Yanjie
Luo, Zhendong
Teng, Fei
author_sort Zhou, Yanjie
collection PubMed
description In this article, we first develop a semi-discretized Crank–Nicolson format about time for the two-dimensional non-stationary Stokes equations about vorticity–stream functions and analyze the existence, uniqueness, stability, and convergence of the semi-discretized Crank–Nicolson solutions. Then we establish a fully discretized Crank–Nicolson finite spectral element format based on the quadrilateral elements for the two-dimensional non-stationary Stokes equations about vorticity–stream functions and analyze the existence, uniqueness, stability, and convergence of the Crank–Nicolson finite spectral element solutions. In the end, we use three numerical examples to confirm the validity of our theoretical conclusions.
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spelling pubmed-62447272018-12-04 A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions Zhou, Yanjie Luo, Zhendong Teng, Fei J Inequal Appl Research In this article, we first develop a semi-discretized Crank–Nicolson format about time for the two-dimensional non-stationary Stokes equations about vorticity–stream functions and analyze the existence, uniqueness, stability, and convergence of the semi-discretized Crank–Nicolson solutions. Then we establish a fully discretized Crank–Nicolson finite spectral element format based on the quadrilateral elements for the two-dimensional non-stationary Stokes equations about vorticity–stream functions and analyze the existence, uniqueness, stability, and convergence of the Crank–Nicolson finite spectral element solutions. In the end, we use three numerical examples to confirm the validity of our theoretical conclusions. Springer International Publishing 2018-11-19 2018 /pmc/articles/PMC6244727/ /pubmed/30839842 http://dx.doi.org/10.1186/s13660-018-1914-5 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhou, Yanjie
Luo, Zhendong
Teng, Fei
A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions
title A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions
title_full A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions
title_fullStr A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions
title_full_unstemmed A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions
title_short A Crank–Nicolson finite spectral element method for the 2D non-stationary Stokes equations about vorticity–stream functions
title_sort crank–nicolson finite spectral element method for the 2d non-stationary stokes equations about vorticity–stream functions
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6244727/
https://www.ncbi.nlm.nih.gov/pubmed/30839842
http://dx.doi.org/10.1186/s13660-018-1914-5
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