Research Article

An optimizing reduced PLSMFE formulation for non-stationary conduction–convection problems

  1. Zhendong Luo1,
  2. Jing Chen2,*,
  3. I. M. Navon3,
  4. Jiang Zhu4

Article first published online: 9 SEP 2008

DOI: 10.1002/fld.1900

Issue

International Journal for Numerical Methods in Fluids

International Journal for Numerical Methods in Fluids

Volume 60, Issue 4, pages 409–436, 10 June 2009

Additional Information

How to Cite

Luo, Z., Chen, J., Navon, I. M. and Zhu, J. (2009), An optimizing reduced PLSMFE formulation for non-stationary conduction–convection problems. International Journal for Numerical Methods in Fluids, 60: 409–436. doi: 10.1002/fld.1900

Author Information

  1. 1

    School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

  2. 2

    College of Science, China Agricultural University, Beijing 100083, China

  3. 3

    School of Computational Science and Department of Mathematics, Florida State University, Dirac Sci. Lib. Bldg., #483, Tallahassee, FL 32306-4120, U.S.A.

  4. 4

    Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China

*College of Science, China Agricultural University, Beijing 100083, China

Publication History

  1. Issue published online: 28 APR 2009
  2. Article first published online: 9 SEP 2008
  3. Manuscript Accepted: 14 JUL 2008
  4. Manuscript Revised: 24 JUN 2008
  5. Manuscript Received: 12 APR 2008

Funded by

  • The National Science Foundation of China. Grant Numbers: 10471100, 40437017, 60573158
  • NASA MAP Grant Modeling, Analysis and Prediction Program. Grant Number: NNG06GC67G

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Keywords:

  • proper orthogonal decomposition;
  • Petrov–Galerkin least squares mixed finite element method;
  • error estimate;
  • non-stationary conduction–convection problems

Abstract

In this paper, proper orthogonal decomposition (POD) is combined with the Petrov–Galerkin least squares mixed finite element (PLSMFE) method to derive an optimizing reduced PLSMFE formulation for the non-stationary conduction–convection problems. Error estimates between the optimizing reduced PLSMFE solutions based on POD and classical PLSMFE solutions are presented. The optimizing reduced PLSMFE formulation can circumvent the constraint of Babuška–Brezzi condition so that the combination of finite element subspaces can be chosen freely and allow optimal-order error estimates to be obtained. Numerical simulation examples have shown that the errors between the optimizing reduced PLSMFE solutions and the classical PLSMFE solutions are consistent with theoretical results. Moreover, they have also shown the feasibility and efficiency of the POD method. Copyright © 2008 John Wiley & Sons, Ltd.

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