Supercloseness of linear finite element method on Vulanović–Bakhvalov mesh for singularly perturbed convection–diffusion equation in 1D

Supercloseness of linear finite element method is studied on the Vulanović–Bakhvalov mesh for a singularly perturbed convection–diffusion problem. A novel interpolation is proposed to tackle challenges arising from the subinterval adjacent to the transition point. This innovative interpolation method is formulated by leveraging the distinctive features of the boundary layer and incorporating the specific attributes of the Vulanović–Bakhvalov mesh. On the basis of that, supercloseness of 2th order can be obtained.