UNCONDITIONAL SUPERCONVERGENT ANALYSIS OF QUASI-WILSON ELEMENT FOR BENJAMIN-BONA-MAHONEY EQUATION

This article aims to study the unconditional superconvergent behavior of nonconformequation. For the generalized rectangular meshes including rectangular mesh, deformed rectangular mesh and piecewise deformed rectangular mesh, by use of the special character of this element, that is, the conforming part(bilinear element) has high accuracy estimates on the generalized rectangular meshes and the consistency error can reach order O(h2), one order higher than its interpolation error, the superconvergent estimates with respect to mesh size h are obtained in the broken H1-norm for the semi-/ fully-discrete schemes. A striking ingredient is that the restrictions between mesh size h and time step tau required in the previous works are removed. Finally, some numerical results are provided to confirm the theoretical analysis.