Abstract
An energy-preserving Crank-Nicolson (CN) fully-discrete scheme is developed with the nonconforming Quasi-Wilson element for the nonlinear Benjamin-Bona-Mahony (BBM) equation. The existence and uniqueness of the numerical solution are demonstrated by the Brouwer fixed point theorem. Then with the help of the special character of this element, that is, the consistency error can reach order O(h2), one order higher than its interpolation error, and the interpolation post-processing technique, the unconditional supercloseness and superconvergence behavior on quadrilateral meshes are derived rigorously without the restriction between mesh size h and time step τ. Finally, some numerical experiments are carried out to confirm the theoretical analysis.
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