Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (5): 647-658.doi: https://doi.org/10.1007/s10483-016-2078-8

• 论文 • 上一篇    下一篇

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

Jincun LIU, Hong LI, Yang LIU, Zhichao FANG   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
  • 收稿日期:2015-10-09 修回日期:2015-10-16 出版日期:2016-05-01 发布日期:2016-05-01
  • 通讯作者: Hong LI E-mail:malhong@imu.edu.cn
  • 基金资助:

    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)

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

Jincun LIU, Hong LI, Yang LIU, Zhichao FANG   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
  • Received:2015-10-09 Revised:2015-10-16 Online:2016-05-01 Published:2016-05-01
  • Contact: Hong LI E-mail:malhong@imu.edu.cn
  • Supported by:

    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)

摘要:

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).

关键词: reduced-order finite element method (FEM), proper orthogonal decomposition (POD), error estimate, fractional Tricomi-type equation, unconditionally stable

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).

Key words: reduced-order finite element method (FEM), proper orthogonal decomposition (POD), error estimate, fractional Tricomi-type equation, unconditionally stable

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