Abstract
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 Q11 and Q01×Q10 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 τ and the subdivision parameter h. Temporal error estimates in H2-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 L2-norm are deduced to bound the numerical solution in L∞-norm. Unconditional superconvergence estimates of un in H1-norm and q→n=∇un in (L2)2-norm with order O(h2+τ2) are obtained. The global superconvergent properties are deduced through above results. Two numerical examples testify the theoretical analysis.
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