Science in China Series A: Mathematics

, Volume 52, Issue 3, pp 585–596

Finite element formulation based on proper orthogonal decomposition for parabolic equations

Article

DOI: 10.1007/s11425-008-0125-9

Cite this article as:
Luo, Z., Chen, J., Sun, P. et al. Sci. China Ser. A-Math. (2009) 52: 585. doi:10.1007/s11425-008-0125-9

Abstract

A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.

Keywords

proper orthogonal decompositionfinite element formulationparabolic equationserror analysis

MSC(2000)

65N3035Q10

Copyright information

© Science in China Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  • ZhenDong Luo
    • 1
    • 2
  • Jing Chen
    • 3
  • Ping Sun
    • 2
  • XiaoZhong Yang
    • 1
  1. 1.School of Mathematics and PhysicsNorth China Electric Power UniversityBeijingChina
  2. 2.School of Mathematics and Computer ScienceGuizhou Normal UniversityGuiyangChina
  3. 3.College of ScienceChina Agricultural UniversityBeijingChina