Geodesic
A priori error estimates of $P^2_0-P_1$ mixed finite element methods for a class of nonlinear parabolic equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 4, pp. 409-424

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In this paper, we consider $P^2_0-P_1$ 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. 
@article{SJVM_2021_24_4_a5,
     author = {Ch. Liu and T. Hou and Zh. Weng},
     title = {A priori error estimates of $P^2_0-P_1$ mixed finite element methods for a class of nonlinear parabolic equations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {409--424},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a5/}
}
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Ch. Liu; T. Hou; Zh. Weng. A priori error estimates of $P^2_0-P_1$ mixed finite element methods for a class of nonlinear parabolic equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 4, pp. 409-424. http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a5/