Supercloseness of finite element method for a singularly perturbed convection-diffusion problem on Bakhvalov-type triangular meshes

We focus on studying supercloseness of linear finite element method on Bakhvalov-type triangular meshes for a singularly perturbed convection-diffusion problem. To achieve the optimal supercloseness result, we introduce a novel interpolation with a simplified structure that is specially designed for the exponential layer part of the solution. This new interpolation is constructed based on the inherent characteristics of the exponential layer function and the structures of Bakhvalov-type triangular meshes. Note that some boundary corrections should be carefully defined to guarantee the homogeneous Dirichlet boundary condition. Furthermore, some integral inequalities also assume a crucial role in our analysis. Finally, supercloseness of almost 3/2th order can be obtained on Bakhvalov-type triangular meshes. This parameter-uniform convergence result is considered optimal for triangular meshes and is supported by numerical experiments.