Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (3): 769-775.

• Articles • Previous Articles     Next Articles

A Reduced Finite Difference Scheme Based on POD Bases and Posteriori Error Estimation for the Three Parabolic Equation

 AN Jing1, LUO Zhen-Dong2   

  1. 1.School of Mathematics and Computer Science, Guizhou Normal University, Guiyang |550001|2.School of Mathematics and Physics, North China Electric Power University, Beijing 102206
  • Received:2008-10-22 Revised:2009-11-30 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    国家自然科学基金(10871188, 10871022)、河北省自然科学基金(A2010001663)和贵州师范大学青年教师科研发展基金资助

Abstract:

In this article, the solution  space of three-dimensional parabolic equation finite difference scheme is studied. Firstly a group of proper orthogonal decomposition (POD) bases of solution space is obtained by using singular value decomposition. Secondly, by combining the Galerkin projection method, the finite difference scheme of three-dimensional parabolic equation is converted into a low
dimensional mode with higher precise. Then, the error between the finite difference scheme solution and the POD scheme solution is
presented. And it is shown by the numerical results that the error between the finite difference scheme solution and the POD scheme solution is consistents with theoretical results. Therefore, the POD method is effective and feasible.

Key words: Solution space, Singular value decomposition and POD basic, Finite difference scheme, Error estimate, Parabolic equation

CLC Number: 

  • 65N30
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