Superconvergence analysis of an energy stable scheme for nonlinear reaction-diffusion equation with BDF mixed FEM

A step-2 backward differential formula (BDF) temporal discretization scheme is constructed for nonlinear reaction-diffusion equation and superconvergence results are studied by mixed finite element method (FEM) with the elements Q(11) and Q(01) x Q(10) unconditionally. In particular, we apply an artificial regularization term to guarantee the energy stability of the step-2 BDF scheme. Splitting technique is utilized to get rid of the ratio between the time step size tau and the subdivision parameter h. Temporal error estimates in H-2-norm are derived by use of the function's monotonicity, which leads to the regularities of the solutions for the time-discrete equations. Spatial error estimates in L-2-norm are deduced to bound the numerical solution in L-infinity-norm. Unconditional superconvergence estimates of u(n) in H-1-norm and (q) over right arrow (n) = del u(n) in (L-2)(2)-norm with order O(h(2) + tau(2)) are obtained. The global superconvergent properties are deduced through above results. Two numerical examples testify the theoretical analysis. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.