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. 
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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/

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