Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains
Provides theoretical convergence guarantees for hp-FEM on a class of problems with boundary and corner layers, which is important for numerical analysis of singularly perturbed PDEs.
The paper proves robust exponential convergence of hp-FEM in balanced and maximum norms for singularly perturbed reaction-diffusion problems on corner domains, using suitably refined meshes.
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 suitable 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.