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• W3046322012 startingPage "1261" @default.
• W3046322012 abstract "This study is mainly concerned with the reduced-order extrapolating technique about the unknown solution coefficient vectors in the Crank-Nicolson finite element (CNFE) method for the parabolic type partial differential equation (PDE). For this purpose, the CNFE method and the existence, stability, and error estimates about the CNFE solutions for the parabolic type PDE are first derived. Next, a reduced-order extrapolating CNFE (ROECNFE) model in matrix-form is established with a proper orthogonal decomposition (POD) method, and the existence, stability, and error estimates of the ROECNFE solutions are proved by matrix theory, resulting in an graceful theoretical development. Specially, our study exposes that the ROECNFE method has the same basis functions and the same accuracy as the CNFE method. Lastly, some numeric tests are shown to computationally verify the validity and correctness about the ROECNFE method." @default.
• W3046322012 created "2020-08-07" @default.
• W3046322012 creator A5014145230 @default.
• W3046322012 date "2020-08-01" @default.
• W3046322012 modified "2023-09-26" @default.
• W3046322012 title "The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation" @default.
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• W3046322012 doi "https://doi.org/10.3390/math8081261" @default.
• W3046322012 hasPublicationYear "2020" @default.
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