Articles

Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation

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  • 1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P. R. China;
    2. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, P. R. China

Received date: 2011-03-24

  Revised date: 2011-04-25

  Online published: 2011-07-03

Supported by

Project supported by the National Natural Science Foundation of China (Nos. 10871022, 11061009, and 40821092), the National Basic Research Program of China (973 Program) (Nos. 2010CB428403, 2009CB421407, and 2010CB951001), and the Natural Science Foundation of Hebei Province of China (No.A2010001663)

Abstract

The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial differential equations (e.g., fluid flows). It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference (FD) scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.

Cite this article

LUO Zhen-Dong;OU Qiu-Lan;XIE Zheng-Hui . Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation[J]. Applied Mathematics and Mechanics, 2011 , 32(7) : 847 -858 . DOI: 10.1007/s10483-011-1464-9

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