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A coupled Newton iterative mixed finite element method for stationary conduction–convection problems

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Abstract

In this paper, a coupled Newton iterative mixed finite element method (MFEM) for solving the stationary conduction–convection problems in two dimension is given. In our method, the Newton iterative MFEM is used for solving all the equations of the conduction–convection problems. The stability and convergence analysis in H 1-norm of \({u_h^n, T_h^n}\) and the L 2-norm of \({p_h^n}\) are derived. The theory analysis shows that our method is stable and have a good precision. Some numerical results are also given, which show that the coupled Newton iterative MFEM is highly efficient for the stationary conduction–convection problems.

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Authors and Affiliations

  1. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Zhiyong Si & Yinnian He

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

    Yinnian He

Authors
  1. Zhiyong Si
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  2. Yinnian He
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Corresponding author

Correspondence to Yinnian He.

Additional information

Communicated by C.C. Douglas.

This work is supported by the NSF of China (10971166) and the National Basic Research Program (No. 2005CB321703).

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Si, Z., He, Y. A coupled Newton iterative mixed finite element method for stationary conduction–convection problems. Computing 89, 1–25 (2010). https://doi.org/10.1007/s00607-010-0093-0

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  • DOI: https://doi.org/10.1007/s00607-010-0093-0

Keywords

Mathematics Subject Classification (2000)