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

Supercloseness in a balanced norm of the NIPG method on Shishkin mesh for a reaction diffusion problem

“…Their typical feature is that one or more layers usually appear in their solutions. To fully resolve the layers and derive the uniform convergence with respect to perturbation parameters, layer-adapted meshes were introduced in the 1960s [15] and gradually became an active research field [5,13]. Due to its simple structure, Shishkin meshes have attracted the attention of many researchers, see [3,4,13].…”

“…In this paper, we focus on the hybridizable discontinuous Galerkin (HDG) method [7], which inherits and develops many advantages of the discontinuous Galerkin (DG) method, such as its applicability to various partial differential equations, its ability to handle complex geometry and support high order accuary, see [8][9][10][11][12][13][14][15][16] for more details. The core advantage of the HDG method lies in expressing the approximate scalar variable and flux element-wise using the approximate trace along the element boundaries, and by enforcing flux continuity to obtain the unique trace at element boundaries.…”