An optimizing reduced PLSMFE formulation for non‐stationary conduction–convection problems |
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| Authors: | Zhendong Luo Jing Chen I. M. Navon Jiang Zhu |
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| Affiliation: | 1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;2. College of Science, China Agricultural University, Beijing 100083, China;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. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China |
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| 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 Babu?ka–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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| Keywords: | proper orthogonal decomposition Petrov– Galerkin least squares mixed finite element method error estimate non‐stationary conduction– convection problems |
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