A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem

作者：Luo, Zhendong^*; Li, Hong; Zhou, Yanjie; Huang, Xiaoming

来源：Journal of Mathematical Analysis and Applications, 2012, 385(1): 310-321.

DOI：10.1016/j.jmaa.2011.06.057

• Proper orthogonal decomposition
• Finite volume element formulation
• Error analysis
• Viscoelastic problem
• Numerical simulation

Proper orthogonal decomposition (POD) method has been successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, i.e., combine a classical finite volume element (FVE) method with POD method to establish a reduced FVE formulation with lower dimensions and sufficiently high accuracy for two-dimensional viscoelastic problem with real practical applied background, and analyze the errors between the reduced POD FVE solution and the classical FVE solution so as to provide scientific theoretic basis for service applications. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is also shown that the reduced FVE formulation based on POD method is feasible and efficient for solving two-dimensional viscoelastic problem.

• 出版日期2012-1-1
• 单位华北电力大学; 北京工商大学; 内蒙古大学; 北京交通大学