Supercloseness of weak Galerkin method on Bakhvalov-type mesh for a singularly perturbed problem in 1D

In this paper, we analyze supercloseness in an energy norm of a weak Galerkin (WG) method on a Bakhvalov-type mesh for a singularly perturbed two-point boundary value problem. For this aim, a special approximation is designed according to the specific structures of the mesh, the WG finite element space and the WG scheme. More specifically, in the interior of each element, the approximation consists of a Gauss-Lobatto interpolant inside the layer and a Gauss-Radau projection outside the layer. On the boundary of each element, the approximation equals the true solution. Besides, with the help of over-penalization technique inside the layer, we prove uniform supercloseness of order k + 1 for the WG method. Numerical experiments verify the supercloseness result and test the influence of different penalization parameters inside the layer.