A Fully Discrete Stabilized Mixed Finite Element Method for Parabolic Problems

In this article, we present a new stabilized mixed finite element method based on the less regularity of flux (velocity) for the two-dimensional parabolic problems in practice. The method combines the Crank-Nicolson scheme with a stabilized mixed finite element method which is based on the velocity projection stabilization method by using the lowest equal-order pair for the velocity and pressure. It is shown that the proposed fully discrete stabilized finite element method results in the optimal error estimates in L 2- and H 1-norm for the pressure and suboptimal error estimate in L 2-norm for the velocity. Finally, we give some numerical experiments to verify the efficiency and theoretical results of this method.