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Modified Characteristics Gauge–Uzawa Finite Element Method for Time Dependent Conduction–Convection Problems

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Abstract

In this paper, we give the modified characteristics Gauge–Uzawa finite element method (MCGUFEM) for time dependent conduction–convection problems, which is gotten by combining the modified characteristics finite element method and the Gauge–Uzawa method. The stability analysis and the error analysis, which shows that our method is stable and has optimal convergence order, are given. In order to show the effect of MCGUFEM, some numerical results are presented. From the numerical results, we can see that MCGUFEM can simulate the fluid field, temperature field and pressure field very well, and MCGUFEM works better for high Grashoff number \(\kappa \) than GUFEM.

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Acknowledgments

The authors would like to thank the editor and the referees for their valuable comments, which led to the improvement of this paper.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454003, People’s Republic of China

    Zhiyong Si & Xiaogang Song

  2. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Pengzhan Huang

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  1. Zhiyong Si
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  2. Xiaogang Song
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Corresponding author

Correspondence to Zhiyong Si.

Additional information

This work is supported by Chinese NSF (Grant No. 11226306), the Doctoral Foundation of Henan Polytechnic University (No. B2012-56) and the Natural Science Foundation of Xinjiang Province (Grant No. 2013211B01).

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Si, Z., Song, X. & Huang, P. Modified Characteristics Gauge–Uzawa Finite Element Method for Time Dependent Conduction–Convection Problems. J Sci Comput 58, 1–24 (2014). https://doi.org/10.1007/s10915-013-9721-0

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  • DOI: https://doi.org/10.1007/s10915-013-9721-0

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Mathematics Subject Classification (2000)