Abstract
In this paper, based on the implicit Euler scheme in the temporal direction, the superconvergence property is investigated by using the special property of the bilinear element on the rectangular mesh for the Sobolev equation with Burgers' nonlinearity. The existence and uniqueness of the fully-discrete solution is proved. Further, the superconvergence error estimate in L∞(H1)-norm is established in terms of a novel approach, i.e., the technique of the combination of the interpolation operator and projection operator. Finally, a numerical experiment is carried out to confirm the theoretical analysis.
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