A new mixed finite element method based on the Crank–Nicolson scheme for the parabolic problems

In this paper, we present a new mixed finite element method based on the less regularity of flux (velocity) for the parabolic problems in practice. Based on this new formulation, we give its corresponding stable conforming finite element approximation for the P02–P1 pair by using Crank–Nicolson time-discretization scheme. Moreover, we derive optimal error estimates in H1-norm and L2-norm for the approximation of pressure p and in L2-norm for the approximation of velocity u. Finally, we give some numerical experiments to verify the efficiency and the theoretical results of the new mixed method.