A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS  

作　　者：罗振东 李磊 孙萍 

机构地区：[1]School of Mathematics and Physics, North China Electric Power University [2]School of Mathematics and Computer Science, Guizhou Normal University

出　　处：《Acta Mathematica Scientia》2013年第5期1471-1484,共14页数学物理学报（B辑英文版）

基　　金：supported by the National Science Foundation of China(11271127 and 11061009);Science Research Program of Guizhou(GJ[2011]2367);the Co-Construction Project of Beijing Municipal Commission of Education

摘　　要：In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.

关 键 词：proper orthogonal decomposition method mixed finite element formulation parabolic equation error estimate 

分 类 号：O175.26[理学—数学]