A new approach of superconvergence analysis for nonlinear BBM equation on anisotropic meshes

A new approach of linear triangular finite element method (FEM) is developed for nonlinear BBM equation on anisotropic meshes. Based on the superclose estimate between the interpolation and Ritz projection of this element together with post-processing technique, the superclose and superconvergence results are derived for the semi-discrete and Crank–Nicolson fully-discrete schemes. Finally, a numerical example is carried out to demonstrate the theoretical analysis.