Before revision:  From this interpolation, error analysis with Lagrange interpolation on the Bakhvalov-type mesh becomes feasible. As a result, we not only prove an optimal convergence between the true solution and the numerical solution, but also get a supercloseness result between the Lagrange interpolant and the numerical solution.
After revision:  From this interpolation, error analysis with Lagrange interpolation on the Bakhvalov-type mesh itself and the weaker exponential layer and obtain an interesting result. Finally, we prove a supercloseness result between the Lagrange interpolant and the numerical solution.