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Reduced-order finite element method based on POD for fractional Tricomi-type equation

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Abstract

The reduced-order finite element method (FEM) based on a proper orthogonal decomposition (POD) theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save memory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element (FE) scheme is shown to be unconditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations (FDEs).

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Jincun Liu, Hong Li, Yang Liu & Zhichao Fang

Authors
  1. Jincun Liu
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  2. Hong Li
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  3. Yang Liu
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  4. Zhichao Fang
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Corresponding author

Correspondence to Hong Li.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11361035 and 11301258) and the Natural Science Foundation of Inner Mongolia (Nos. 2012MS0106 and 2012MS0108)

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Liu, J., Li, H., Liu, Y. et al. Reduced-order finite element method based on POD for fractional Tricomi-type equation. Appl. Math. Mech.-Engl. Ed. 37, 647–658 (2016). https://doi.org/10.1007/s10483-016-2078-8

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  • DOI: https://doi.org/10.1007/s10483-016-2078-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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