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

作者：Luo, Zhendong^*; Li, Lei; Sun, Ping

来源：Acta Mathematica Scientia, 2013, 33(5): 1471-1484.

DOI：10.1016/s0252-9602(13)60097-1

• proper orthogonal decomposition method
• mixed finite element formulation
• parabolic equation
• error estimate

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-Babuska 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 consistent 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.

• 出版日期2013-9
• 单位贵州师范大学; 华北电力大学; 华北电力大学（保定）