Supercloseness of the NIPG method on Bakhvalov-type meshes for a system of singularly perturbed reaction-diffusion equations

In this paper, a higher order nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov mesh is developed for a weakly coupled system of singularly perturbed reaction-diffusion equations. At first, by selecting special penalty parameters at different mesh points, the supercloseness of the $k+\frac{1}{2}$ order of our proposed method is derived, where $k$ is the degree of polynomials space. Then, an optimal order of uniform convergence analysis in a balanced norm is performed. Finally, some numerical experiments are given to support our theoretical findings.