Unconditional Superconvergent Analysis of Quasi-Wilson Element for Benjamin-Bona-Mahoney Equation (Journal of Computational Mathematics, 2022)
This article aims to study the unconditional superconvergent behavior of nonconforming quadrilateral quasi-Wilson element for nonlinear Benjamin Bona Mahoney (BBM) equation. 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 $O(h^2)$, one order higher than its interpolation error, the superconvergent estimates with respect to mesh size $h$ are obtained in the broken $H^1$-norm for the semi-/ fully-discrete schemes. A striking ingredient is that the restrictions between mesh size $h$ and time step $τ$ required in the previous works are removed. Finally, some numerical results are provided to confirm the theoretical analysis.
Keywords: BBM equations; Quasi-Wilson element; Superconvergent behavior; Semi- and fully-discrete schemes; Unconditionally.