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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2021, Volume 24, Number 4, Pages 409–424
DOI: https://doi.org/10.15372/SJNM20210405 (Mi sjvm789) 		 
A priori error estimates of P20−P1 mixed finite element methods for a class of nonlinear parabolic equations

Ch. Liua, T. Houb, Zh. Wengc

a College of Science, Hunan University of Science and Engineering, Yongzhou 425199, Hunan, China
b School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin, China
c School of Mathematics Science, Huaqiao University, Quanzhou 362021, Fujian, China
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DOI: https://doi.org/10.15372/SJNM20210405
Abstract: In this paper, we consider P20−P1 mixed finite element approximations of a class of nonlinear parabolic equations. The backward Euler scheme for temporal discretization is used. Firstly, a new mixed projection is defined and the related a priori error estimates are proved. Secondly, optimal a priori error estimates for pressure variable and velocity variable are derived. Finally, a numerical example is presented to verify the theoretical results.
Key words: nonlinear parabolic equations, P20−P1 mixed finite element method, a priori error estimates, square integrable function space.
Funding agency Grant number
National Natural Science Foundation of China 11901189
11701197
Natural Science Foundation of Jilin Province JJKH20190634KJ
Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University ZQN-YX502
The first author is supported by the National Natural Science Foundation of China (11901189), the Key Project of Hunan Provincial Education Department (19A191), and the construct program of applied characteristic discipline at the Hunan University of Science and Engineering. The second author is supported by the Science and Technology Research Project of the Jilin Provincial Department of Education (JJKH20190634KJ). The third author is supported by the National Natural Science Foundation of China (11701197) and the Promotion Program for Young and Middle-aged Teachers in Science and Technology Research of the Huaqiao University (ZQN-YX502).
Received: 30.06.2020
Revised: 18.09.2020
Accepted: 14.07.2021
English version:
Numerical Analysis and Applications, 2021, Volume 14, Issue 4, Pages 357–371
DOI: https://doi.org/10.1134/S1995423921040054
Bibliographic databases:
Document Type: Article
MSC: 49J20, 65N30
Language: Russian
Citation: Ch. Liu, T. Hou, Zh. Weng, “A priori error estimates of P20−P1 mixed finite element methods for a class of nonlinear parabolic equations”, Sib. Zh. Vychisl. Mat., 24:4 (2021), 409–424; Num. Anal. Appl., 14:4 (2021), 357–371
Citation in format AMSBIB
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\pages 409--424
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\pages 357--371
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