Abstract
In this paper, an implicit Crank-Nicolson (CN) formula of the mixed finite element method (FEM) is developed with the bilinear finite element for nonlinear fourth-order Rosenau equation. The stability, existence and uniqueness of the approximate solution of this scheme are proved. Then, unconditional superclose and superconvergence estimates of order O(h2+τ2) in H1-norm are derived by the combination technique of interpolation and projection. Finally, some numerical results confirm our theoretical analysis. Here and later h and τ denote the mesh size and the time step, respectively.
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