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A Priori Error Estimates of \(P_0^2{-}P_1\) Mixed Finite Element Methods for a Class of Nonlinear Parabolic Equations

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Abstract

In this paper, we consider \(P_0^2{-}P_1\) mixed finite element approximations of a class of nonlinear parabolic equations. The backward Euler scheme for temporal discretization is used. Firstly, the new mixed projection is defined and the related a priori error estimates are proved. Secondly, the optimal a priori error estimates for the pressure variable and the velocity variable are derived. Finally, a numerical example is presented to verify the theoretical results.

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Authors and Affiliations

  1. College of Science, Hunan University of Science and Engineering, 425199, Yongzhou, Hunan, China

    Ch. Liu

  2. School of Mathematics and Statistics, Beihua University, 132013, Jilin, Jilin, China

    T. Hou

  3. School of Mathematics Science, Huaqiao University, 362021, Quanzhou, Fujian, China

    Zh. Weng

Authors
  1. Ch. Liu
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  2. T. Hou
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  3. Zh. Weng
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Correspondence to Ch. Liu, T. Hou or Zh. Weng.

Additional information

Translated from Sibirskii Zhurnal Vychislitel’noi Matematiki, 2021, Vol. 24, No. 4, pp. 409-424. https://doi.org/10.15372/SJNM20210405.

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Liu, C., Hou, T. & Weng, Z. A Priori Error Estimates of \(P_0^2{-}P_1\) Mixed Finite Element Methods for a Class of Nonlinear Parabolic Equations. Numer. Analys. Appl. 14, 357–371 (2021). https://doi.org/10.1134/S1995423921040054

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  • DOI: https://doi.org/10.1134/S1995423921040054

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