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

The reduced-order finite element method （FEM） based on a proper orthogo- nal 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 mem- ory space and effectively relieve the computing loa...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2016-05, Vol.37 (5), p.647-658
Main Authors: Liu, Jincun, Li, Hong, Liu, Yang, Fang, Zhichao
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical Mechanics
Fluid- and Aerodynamics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
POD
Tricomi方程
内存空间
分数阶微分方程
有限元法
条件稳定
误差估计
降阶
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Summary:The reduced-order finite element method （FEM） based on a proper orthogo- nal 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 mem- ory 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 un- conditionally 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）.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-016-2078-8