Supercloseness analysis of the nonsymmetric interior penalty Galerkin method for a singularly perturbed problem on Bakhvalov-type mesh

Abstract

For a singularly perturbed convection diffusion problem, we study the supercloseness of the nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov-type mesh. In this process, a new composite interpolation is designed, which consists of Gauß Radau projection outside the layer and Gauß Lobatto projection inside the layer. Then by choosing the penalty parameters at different mesh points, we derive the supercloseness of k+12th order (k≥1) in an energy norm.