A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions

A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions

Abstract In this study, a time semi-discretized Crank–Nicolson (CN) scheme of the two-dimensional (2D) unsteady conduction–convection problems for vorticity and stream functions is first built together with showing the existence and stability along with error estimates to the semi-discretized CN sol...

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Main Authors: Fei Teng, Taiying Zhu, Zhendong Luo
Format: Article
Language:English
Published: SpringerOpen 2020-01-01
Series:Journal of Inequalities and Applications
Subjects:
Semi-discretized Crank–Nicolson scheme as a function of time
Unsteady conduction–convection problems with vorticity and stream functions
Spectral element Crank–Nicolson model
Error estimates
Online Access:https://doi.org/10.1186/s13660-020-2288-z
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spelling doaj-1c704e008ef441ba8c9965ba4f61e2e52021-01-31T12:08:36ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-01-012020111810.1186/s13660-020-2288-zA spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functionsFei Teng0Taiying Zhu1Zhendong Luo2College of Arts and Sciences, Shanghai Dianji UniversityCollege of Arts and Sciences, Shanghai Dianji UniversitySchool of Mathematics and Physics, North China Electric Power UniversityAbstract In this study, a time semi-discretized Crank–Nicolson (CN) scheme of the two-dimensional (2D) unsteady conduction–convection problems for vorticity and stream functions is first built together with showing the existence and stability along with error estimates to the semi-discretized CN solutions. Afterwards, a fully discretized spectral element CN (SECN) model of the 2D unsteady conduction–convection problems as regards the vorticity and stream functions is set up together with showing the proof of the existence and stability along with error estimates of the SECN solution. Lastly, a set of numerical experiments are offered for checking the correctness of the theoretical conclusions.https://doi.org/10.1186/s13660-020-2288-zSemi-discretized Crank–Nicolson scheme as a function of timeUnsteady conduction–convection problems with vorticity and stream functionsSpectral element Crank–Nicolson modelError estimates
collection DOAJ
language English
format Article
sources DOAJ
author Fei Teng
Taiying Zhu
Zhendong Luo
spellingShingle Fei Teng
Taiying Zhu
Zhendong Luo
A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions
Journal of Inequalities and Applications
Semi-discretized Crank–Nicolson scheme as a function of time
Unsteady conduction–convection problems with vorticity and stream functions
Spectral element Crank–Nicolson model
Error estimates
author_facet Fei Teng
Taiying Zhu
Zhendong Luo
author_sort Fei Teng
title A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions
title_short A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions
title_full A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions
title_fullStr A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions
title_full_unstemmed A spectral element Crank–Nicolson model to the 2D unsteady conduction–convection problems about vorticity and stream functions
title_sort spectral element crank–nicolson model to the 2d unsteady conduction–convection problems about vorticity and stream functions
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1029-242X
publishDate 2020-01-01
description Abstract In this study, a time semi-discretized Crank–Nicolson (CN) scheme of the two-dimensional (2D) unsteady conduction–convection problems for vorticity and stream functions is first built together with showing the existence and stability along with error estimates to the semi-discretized CN solutions. Afterwards, a fully discretized spectral element CN (SECN) model of the 2D unsteady conduction–convection problems as regards the vorticity and stream functions is set up together with showing the proof of the existence and stability along with error estimates of the SECN solution. Lastly, a set of numerical experiments are offered for checking the correctness of the theoretical conclusions.
topic Semi-discretized Crank–Nicolson scheme as a function of time
Unsteady conduction–convection problems with vorticity and stream functions
Spectral element Crank–Nicolson model
Error estimates
url https://doi.org/10.1186/s13660-020-2288-z
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AT taiyingzhu aspectralelementcranknicolsonmodeltothe2dunsteadyconductionconvectionproblemsaboutvorticityandstreamfunctions
AT zhendongluo aspectralelementcranknicolsonmodeltothe2dunsteadyconductionconvectionproblemsaboutvorticityandstreamfunctions
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