Abstract
In this paper, the constrained nonconforming rotated Q1 (CNQ1rot) element is employed to study the superconvergence behavior of the backward-Euler (B-E) and Crank–Nicolson (C–N) fully-discrete schemes for the parabolic equation. By applying the mean-value and integral identities techniques, a novel high-accuracy estimate for the CNQ1rot element is proved on anisotropic meshes rigorously, which is essential to derive the superclose result. Then, the superconvergence results for the above two schemes are deduced with the help of the interpolation post-processing approach, respectively. Eventually, some numerical experiments are carried out to verify the rationality of the theoretical analysis.
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