A reduced-order extrapolated approach to solution coefficient vectors in the Crank-Nicolson finite element method for the uniform transmission line equation |
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Authors: | Fei Teng Zhendong Luo |
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Affiliation: | 1. College of Arts and Sciences, Shanghai Dianji University, 201306 Shanghai, China;2. School of Mathematics and Physics, North China Electric Power University, 102206 Beijing, China |
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Abstract: | This work is concerned mainly with developing and testing the reduced-order extrapolated approach to the unknown coefficient vectors in the Crank-Nicolson finite element (CNFE) solutions for the uniform transmission line equation. For this objective, the CNFE functional and matrix models and the existence, stability, and errors of the CNFE solutions of the uniform transmission line equation are first derived. Then a reduced-order extrapolated CNFE (ROECNFE) matrix model is established by means of a proper orthogonal decomposition technique, and the existence, stability, and error estimates of the ROECNFE solutions are demonstrated by matrix analysis, leading to an elegant theoretical development. Especially, our work shows that the basis functions and accuracy of the ROECNFE matrix model are the same as those of the CNFE matrix model. Finally, some numerical tests are illustrated to computationally experimentally confirm the validity and sharpness of the ROECNFE method. |
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Keywords: | Crank-Nicolson finite element method Uniform transmission line equation Proper orthogonal decomposition Reduced-order extrapolated Crank-Nicolson finite element matrix model Existence and stability as well as error estimate |
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