Supercloseness in a balanced norm of the NIPG method on Bakhvalov-type meshes for a reaction diffusion problem

For numerical methods applied to singularly perturbed reaction-diffusion problems, the balanced norm has emerged as an effective tool. In this manuscript, we analyze supercloseness properties in the balanced norm for the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh. To achieve this, we construct a novel interpolant that combines the Lagrange interpolant and a local weighted $L^2$ projection. Furthermore, by appropriately defining penalty parameters at the nodal points of the Bakhvalov-type mesh, we establish supercloseness of almost order $k+1$ in most cases.