A priori error estimates of $P^2_0-P_1$ mixed finite element methods for a class of nonlinear parabolic equations

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.