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

doi:10.1007/s10483-016-2078-8

Abstract

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

2010 MSC Number:

Jincun LIU, Hong LI, Yang LIU, Zhichao FANG. Reduced-order finite element method based on POD for fractional Tricomi-type equation. Applied Mathematics and Mechanics (English Edition), 2016, 37(5): 647-658.

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