Abstract
In this paper, two modified nonconforming finite element fully discrete schemes are considered for solving the nonlinear Burgers' equation. The schemes are constructed by using the nonconforming Wilson element approximation in space combining with the backward Euler(BE) and 2-step backward differentiation formula (BDF2) respectively in time. We present the superconvergence results of the two proposed schemes in modified energy norm of order O(h2+τ) and O(h2+τ2), where h and τ are the space subdivision parameter and time step respectively. The proof involves the time-space error splitting technique, the discrete embedding inequality, the technique of taking difference between two time, the discrete derivative transfer technique and a new modified projection operator. Our analysis not only gets rid of the restriction between temporal and spatial step sizes, but also provides one order higher error estimate results than that of corresponding traditional finite element fully discrete schemes. Finally, numerical experiments are carried out to demonstrate the effective of theoretical analysis.
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