Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation

For convenience, this study mainly focuses on the reduced order of coefficient vectors for the classical finite spectral element Crank–Nicolson (CFSECN) solutions about the two‐dimensional (2D) nonstationary Stokes problem, resulting that the reduced order model can possess the same basis functions...

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Veröffentlicht in:Numerical methods for partial differential equations Jg. 39; H. 4; S. 2823 - 2839
Hauptverfasser: Luo, Zhendong, Liu, Xiangdong, Zeng, Yihui, Li, Yuejie
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Hoboken, USA John Wiley & Sons, Inc 01.07.2023
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Schlagworte:
Basis functions
existence and stability as well as error estimation
Extrapolation
finite spectral element Crank–Nicolson solution
Fluid mechanics
Mathematical models
nonstationary Stokes problem
Proper Orthogonal Decomposition
Reduced order models
Stability analysis
Stream functions (fluids)
Vorticity
ISSN:0749-159X, 1098-2426
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Zusammenfassung:For convenience, this study mainly focuses on the reduced order of coefficient vectors for the classical finite spectral element Crank–Nicolson (CFSECN) solutions about the two‐dimensional (2D) nonstationary Stokes problem, resulting that the reduced order model can possess the same basis functions together with same precision as the CFSECN one. To this end, the CFSECN format of the 2D nonstationary Stokes problem about vorticity function and stream function and, the existence and stability as well as error estimations for the CFSECN solutions are first proposed. Afterwards, a reduced order extrapolation finite spectral element Crank–Nicolson (ROEFSECN) model is created by means of proper orthogonal decomposition method, and the existence together with stability as well as errors of the ROEFSECN solutions is analyzed by the matrix tool, resulting that the theory analysis turns into very simple. Finally, two numerical examples are provided to confirm the correctness for the theory consequences. Therefore, the study is absolutely distinguished from the existed ones.
Bibliographie:Funding information
National Natural Science Foundation of China, 11671106; Ordos Science and Technology Plan Project, 2022YY041; Inner Mongolia Natural Science Foundation, 2019MS06013
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ISSN:0749-159X
1098-2426
DOI:10.1002/num.22989