Abstract
AbstractA three step backward differential formula scheme is proposed for nonlinear reaction–diffusion equation and superconvergence results are studied with Galerkin finite element method unconditionally. Energy stability is testified for the constructed scheme with an artificial term. Splitting technique is utilized to get rid of the ratio between the time step size and the subdivision parameter . Temporal error estimate in H2‐norm is derived, which leads to the boundedness of the solutions of the time‐discrete equations. Unconditional spatial error estimate in L2‐norm is deduced which help bound the numerical solutions in L∞‐norm. Superconvergent property of in H1‐norm with order is obtained by taking difference between two time levels of the error equations unconditionally. The global superconvergent property is deduced through the above results. Two numerical examples show the validity of the theoretical analysis.
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