(untitled) (Journal of Computational Mathematics, 2018)
This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair Q_11/Q_01 × Q_10 as an example, a new mixed finite element method (FEM) is established and the τ -independent superclose results of the original variable u in H^1-norm and the flux variable q ^→= −a(u)∇u in L^2-norm are deduced (τ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.