Robust exponential convergence of [formula omitted]-FEM in balanced norms for singularly perturbed reaction–diffusion problems: Corner domains

Abstract

The hp-version of the finite element method is applied to singularly perturbed reaction–diffusion type equations on polygonal domains. The solution exhibits boundary layers as well as corner layers. On a class of meshes that are suitably refined near the boundary and the corners, robust exponential convergence (in the polynomial degree) is shown in both a balanced norm and the maximum norm.