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A new mixed finite element method based on the Crank-Nicolson scheme for Burgers’ equation

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Abstract

In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers’ equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the P 20 − P 1 pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P.R. China

    Xiaohui Hu, Pengzhan Huang & Xinlong Feng

Authors
  1. Xiaohui Hu
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  2. Pengzhan Huang
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  3. Xinlong Feng
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Corresponding author

Correspondence to Pengzhan Huang.

Additional information

The research has been supported by the NSF of China (Grant No. 11401511 and 11271313) and the Scientific Research Program of the Higher Education Institution of Xinjiang (Grant No. XJEDU2014S002).

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Hu, X., Huang, P. & Feng, X. A new mixed finite element method based on the Crank-Nicolson scheme for Burgers’ equation. Appl Math 61, 27–45 (2016). https://doi.org/10.1007/s10492-016-0120-3

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  • DOI: https://doi.org/10.1007/s10492-016-0120-3

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